Parabolic Geometries Associated with Differential Equations of Finite Type
Identifieur interne : 000325 ( Istex/Corpus ); précédent : 000324; suivant : 000326Parabolic Geometries Associated with Differential Equations of Finite Type
Auteurs : Keizo Yamaguchi ; Tomoaki YatsuiSource :
- Progress in Mathematics ; 2007.
Abstract
Abstract: We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.
Url:
DOI: 10.1007/978-0-8176-4530-4_11
Links to Exploration step
ISTEX:0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Parabolic Geometries Associated with Differential Equations of Finite Type</title><author><name sortKey="Yamaguchi, Keizo" sort="Yamaguchi, Keizo" uniqKey="Yamaguchi K" first="Keizo" last="Yamaguchi">Keizo Yamaguchi</name><affiliation><mods:affiliation>Department of Mathematics, Graduate School of Science, Hokkaido University, 060-0810, Sapporo, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: yamaguch@math.sci.hokudai.ac.jp</mods:affiliation></affiliation></author><author><name sortKey="Yatsui, Tomoaki" sort="Yatsui, Tomoaki" uniqKey="Yatsui T" first="Tomoaki" last="Yatsui">Tomoaki Yatsui</name><affiliation><mods:affiliation>Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, 070-8621, Asahikawa, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: tomoaki@asa.hokkyodai.ac.jp</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/978-0-8176-4530-4_11</idno><idno type="url">https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000325</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000325</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Parabolic Geometries Associated with Differential Equations of Finite Type</title><author><name sortKey="Yamaguchi, Keizo" sort="Yamaguchi, Keizo" uniqKey="Yamaguchi K" first="Keizo" last="Yamaguchi">Keizo Yamaguchi</name><affiliation><mods:affiliation>Department of Mathematics, Graduate School of Science, Hokkaido University, 060-0810, Sapporo, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: yamaguch@math.sci.hokudai.ac.jp</mods:affiliation></affiliation></author><author><name sortKey="Yatsui, Tomoaki" sort="Yatsui, Tomoaki" uniqKey="Yatsui T" first="Tomoaki" last="Yatsui">Tomoaki Yatsui</name><affiliation><mods:affiliation>Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, 070-8621, Asahikawa, Japan</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: tomoaki@asa.hokkyodai.ac.jp</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="s">Progress in Mathematics</title><imprint><date>2007</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><author><json:item><name>Keizo Yamaguchi</name><affiliations><json:string>Department of Mathematics, Graduate School of Science, Hokkaido University, 060-0810, Sapporo, Japan</json:string><json:string>E-mail: yamaguch@math.sci.hokudai.ac.jp</json:string></affiliations></json:item><json:item><name>Tomoaki Yatsui</name><affiliations><json:string>Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, 070-8621, Asahikawa, Japan</json:string><json:string>E-mail: tomoaki@asa.hokkyodai.ac.jp</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-XH40HZCT-P</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.</abstract><qualityIndicators><score>7.792</score><pdfWordCount>22372</pdfWordCount><pdfCharCount>74281</pdfCharCount><pdfVersion>1.3</pdfVersion><pdfPageCount>49</pdfPageCount><pdfPageSize>441 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><abstractWordCount>66</abstractWordCount><abstractCharCount>465</abstractCharCount><keywordCount>0</keywordCount></qualityIndicators><title>Parabolic Geometries Associated with Differential Equations of Finite Type</title><chapterId><json:string>11</json:string><json:string>Chap11</json:string></chapterId><genre><json:string>research-article</json:string></genre><serie><title>Progress in Mathematics</title><language><json:string>unknown</json:string></language><copyrightDate>2007</copyrightDate><volume>Part III</volume><editor><json:item><name>Hyman Bass</name></json:item><json:item><name>Joseph Oesterlé</name></json:item></editor><author><json:item><name>Alan Weinstein</name></json:item></author></serie><host><title>From Geometry to Quantum Mechanics</title><language><json:string>unknown</json:string></language><copyrightDate>2007</copyrightDate><doi><json:string>10.1007/978-0-8176-4530-4</json:string></doi><eisbn><json:string>978-0-8176-4530-4</json:string></eisbn><bookId><json:string>978-0-8176-4530-4</json:string></bookId><isbn><json:string>978-0-8176-4512-0</json:string></isbn><volume>252</volume><pages><first>161</first><last>209</last></pages><genre><json:string>book-series</json:string></genre><editor><json:item><name>Yoshiaki Maeda</name><affiliations><json:string>Department of Mathematics, Faculty of Science and Technology, Keio University, 223-8522, Hiyoshi, Yokohama, Japan</json:string></affiliations></json:item><json:item><name>Takushiro Ochiai</name><affiliations><json:string>Department of Natural Science, Nippon Sports Science University, 7-1-1, Fukazawa, Setagaya-ku, 158-8508, Tokyo, Japan</json:string></affiliations></json:item><json:item><name>Peter Michor</name><affiliations><json:string>Facultät für Mathematik, Universität Wein, Nordbergstrasse 15, A-1090, Wein, Austria</json:string></affiliations></json:item><json:item><name>Akira Yoshioka</name><affiliations><json:string>Department of Mathematics, Tokyo University of Science, 102-8601, Kagurazaka, Tokyo, Japan</json:string></affiliations></json:item></editor><subject><json:item><value>Mathematics and Statistics</value></json:item><json:item><value>Mathematics</value></json:item><json:item><value>Differential Geometry</value></json:item><json:item><value>Geometry</value></json:item><json:item><value>Analysis</value></json:item><json:item><value>Topological Groups, Lie Groups</value></json:item><json:item><value>Mathematical Methods in Physics</value></json:item><json:item><value>Quantum Physics</value></json:item></subject></host><ark><json:string>ark:/67375/HCB-XH40HZCT-P</json:string></ark><publicationDate>2007</publicationDate><copyrightDate>2007</copyrightDate><doi><json:string>10.1007/978-0-8176-4530-4_11</json:string></doi><id>0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816</id><score>1</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Parabolic Geometries Associated with Differential Equations of Finite Type</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher scheme="https://publisher-list.data.istex.fr">Birkhäuser Boston</publisher><pubPlace>Boston, MA</pubPlace><availability><licence><p>Birkhäuser Boston, 2007</p></licence><p scheme="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</p></availability><date>2007</date></publicationStmt><notesStmt><note type="research-article" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</note><note type="book-series" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Parabolic Geometries Associated with Differential Equations of Finite Type</title><author xml:id="author-0000"><persName><forename type="first">Keizo</forename><surname>Yamaguchi</surname></persName><email>yamaguch@math.sci.hokudai.ac.jp</email><affiliation>Department of Mathematics, Graduate School of Science, Hokkaido University, 060-0810, Sapporo, Japan</affiliation></author><author xml:id="author-0001"><persName><forename type="first">Tomoaki</forename><surname>Yatsui</surname></persName><email>tomoaki@asa.hokkyodai.ac.jp</email><affiliation>Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, 070-8621, Asahikawa, Japan</affiliation></author><idno type="istex">0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816</idno><idno type="ark">ark:/67375/HCB-XH40HZCT-P</idno><idno type="DOI">10.1007/978-0-8176-4530-4_11</idno><idno type="ChapterID">11</idno><idno type="ChapterID">Chap11</idno></analytic><monogr><title level="m">From Geometry to Quantum Mechanics</title><title level="m" type="sub">In Honor of Hideki Omori</title><idno type="DOI">10.1007/978-0-8176-4530-4</idno><idno type="pISBN">978-0-8176-4512-0</idno><idno type="eISBN">978-0-8176-4530-4</idno><idno type="book-title-id">116157</idno><idno type="book-id">978-0-8176-4530-4</idno><idno type="book-chapter-count">16</idno><idno type="book-volume-number">252</idno><idno type="book-sequence-number">252</idno><idno type="PartChapterCount">5</idno><editor xml:id="book-author-0000"><persName><forename type="first">Yoshiaki</forename><surname>Maeda</surname></persName><affiliation>Department of Mathematics, Faculty of Science and Technology, Keio University, 223-8522, Hiyoshi, Yokohama, Japan</affiliation></editor><editor xml:id="book-author-0001"><persName><forename type="first">Takushiro</forename><surname>Ochiai</surname></persName><affiliation>Department of Natural Science, Nippon Sports Science University, 7-1-1, Fukazawa, Setagaya-ku, 158-8508, Tokyo, Japan</affiliation></editor><editor xml:id="book-author-0002"><persName><forename type="first">Peter</forename><surname>Michor</surname></persName><affiliation>Facultät für Mathematik, Universität Wein, Nordbergstrasse 15, A-1090, Wein, Austria</affiliation></editor><editor xml:id="book-author-0003"><persName><forename type="first">Akira</forename><surname>Yoshioka</surname></persName><affiliation>Department of Mathematics, Tokyo University of Science, 102-8601, Kagurazaka, Tokyo, Japan</affiliation></editor><imprint><publisher>Birkhäuser Boston</publisher><pubPlace>Boston, MA</pubPlace><date type="published" when="2007"></date><biblScope unit="volume">252</biblScope><biblScope unit="page" from="161">161</biblScope><biblScope unit="page" to="209">209</biblScope></imprint></monogr><series><title level="s">Progress in Mathematics</title><editor xml:id="serie-author-0000"><persName><forename type="first">Hyman</forename><surname>Bass</surname></persName></editor><editor xml:id="serie-author-0001"><persName><forename type="first">Joseph</forename><surname>Oesterlé</surname></persName></editor><editor xml:id="serie-author-0002"><persName><forename type="first">Alan</forename><surname>Weinstein</surname></persName></editor><biblScope><date>2007</date></biblScope><biblScope unit="part">Part III</biblScope><idno type="series-id">4848</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2007</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11649</label><item><term>Mathematics and Statistics</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>SCM</label><label>SCM21022</label><label>SCM21006</label><label>SCM12007</label><label>SCM11132</label><label>SCP19013</label><label>SCP19080</label><item><term>Mathematics</term></item><item><term>Differential Geometry</term></item><item><term>Geometry</term></item><item><term>Analysis</term></item><item><term>Topological Groups, Lie Groups</term></item><item><term>Mathematical Methods in Physics</term></item><item><term>Quantum Physics</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2007">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-11-28">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-ebooks not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Birkhäuser Boston</PublisherName><PublisherLocation>Boston, MA</PublisherLocation></PublisherInfo><Series><SeriesInfo SeriesType="Series" TocLevels="0"><SeriesID>4848</SeriesID><SeriesTitle Language="En">Progress in Mathematics</SeriesTitle></SeriesInfo><SeriesHeader><AuthorGroup><Author><AuthorName DisplayOrder="Western"><GivenName>Alan</GivenName><FamilyName>Weinstein</FamilyName></AuthorName></Author></AuthorGroup><EditorGroup><Editor><EditorName DisplayOrder="Western"><GivenName>Hyman</GivenName><FamilyName>Bass</FamilyName></EditorName></Editor><Editor><EditorName DisplayOrder="Western"><GivenName>Joseph</GivenName><FamilyName>Oesterlé</FamilyName></EditorName></Editor></EditorGroup></SeriesHeader><Book Language="En"><BookInfo BookProductType="Contributed volume" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="Unnumbered" TocLevels="0"><BookID>978-0-8176-4530-4</BookID><BookTitle>From Geometry to Quantum Mechanics</BookTitle><BookSubTitle>In Honor of Hideki Omori</BookSubTitle><BookVolumeNumber>252</BookVolumeNumber><BookSequenceNumber>252</BookSequenceNumber><BookDOI>10.1007/978-0-8176-4530-4</BookDOI><BookTitleID>116157</BookTitleID><BookPrintISBN>978-0-8176-4512-0</BookPrintISBN><BookElectronicISBN>978-0-8176-4530-4</BookElectronicISBN><BookChapterCount>16</BookChapterCount><BookCopyright><CopyrightHolderName>Birkhäuser Boston</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="SCM" Type="Primary">Mathematics</BookSubject><BookSubject Code="SCM21022" Priority="1" Type="Secondary">Differential Geometry</BookSubject><BookSubject Code="SCM21006" Priority="2" Type="Secondary">Geometry</BookSubject><BookSubject Code="SCM12007" Priority="3" Type="Secondary">Analysis</BookSubject><BookSubject Code="SCM11132" Priority="4" Type="Secondary">Topological Groups, Lie Groups</BookSubject><BookSubject Code="SCP19013" Priority="5" Type="Secondary">Mathematical Methods in Physics</BookSubject><BookSubject Code="SCP19080" Priority="6" Type="Secondary">Quantum Physics</BookSubject><SubjectCollection Code="SUCO11649">Mathematics and Statistics</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff1"><EditorName DisplayOrder="Western"><GivenName>Yoshiaki</GivenName><FamilyName>Maeda</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff2"><EditorName DisplayOrder="Western"><GivenName>Takushiro</GivenName><FamilyName>Ochiai</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff3"><EditorName DisplayOrder="Western"><GivenName>Peter</GivenName><FamilyName>Michor</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Akira</GivenName><FamilyName>Yoshioka</FamilyName></EditorName></Editor><Affiliation ID="Aff1"><OrgDivision>Department of Mathematics, Faculty of Science and Technology</OrgDivision><OrgName>Keio University</OrgName><OrgAddress><City>Hiyoshi, Yokohama</City><Postcode>223-8522</Postcode><Country>Japan</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Department of Natural Science</OrgDivision><OrgName>Nippon Sports Science University</OrgName><OrgAddress><Street>7-1-1, Fukazawa, Setagaya-ku</Street><City>Tokyo</City><Postcode>158-8508</Postcode><Country>Japan</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgDivision>Facultät für Mathematik</OrgDivision><OrgName>Universität Wein</OrgName><OrgAddress><Street>Nordbergstrasse 15</Street><Postcode>A-1090</Postcode><City>Wein</City><Country>Austria</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>Tokyo University of Science</OrgName><OrgAddress><City>Kagurazaka, Tokyo</City><Postcode>102-8601</Postcode><Country>Japan</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part3"><PartInfo TocLevels="0"><PartID>3</PartID><PartNumber>Part III</PartNumber><PartSequenceNumber>3</PartSequenceNumber><PartTitle>Symplectic Geometry and Poisson Geometry</PartTitle><PartChapterCount>5</PartChapterCount><PartContext><SeriesID>4848</SeriesID><BookID>978-0-8176-4530-4</BookID><BookTitle>From Geometry to Quantum Mechanics</BookTitle></PartContext></PartInfo><Chapter ID="Chap11" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" Language="En" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>11</ChapterID><ChapterDOI>10.1007/978-0-8176-4530-4_11</ChapterDOI><ChapterSequenceNumber>11</ChapterSequenceNumber><ChapterTitle Language="En">Parabolic Geometries Associated with Differential Equations of Finite Type</ChapterTitle><ChapterFirstPage>161</ChapterFirstPage><ChapterLastPage>209</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Birkhäuser Boston</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>4848</SeriesID><PartID>3</PartID><BookID>978-0-8176-4530-4</BookID><BookTitle>From Geometry to Quantum Mechanics</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff5"><AuthorName DisplayOrder="Western"><GivenName>Keizo</GivenName><FamilyName>Yamaguchi</FamilyName></AuthorName><Contact><Email>yamaguch@math.sci.hokudai.ac.jp</Email></Contact></Author><Author AffiliationIDS="Aff6"><AuthorName DisplayOrder="Western"><GivenName>Tomoaki</GivenName><FamilyName>Yatsui</FamilyName></AuthorName><Contact><Email>tomoaki@asa.hokkyodai.ac.jp</Email></Contact></Author><Affiliation ID="Aff5"><OrgDivision>Department of Mathematics, Graduate School of Science</OrgDivision><OrgName>Hokkaido University</OrgName><OrgAddress><City>Sapporo</City><Postcode>060-0810</Postcode><Country>Japan</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>Hokkaido University of Education</OrgName><OrgAddress><Street>Asahikawa Campus</Street><City>Asahikawa</City><Postcode>070-8621</Postcode><Country>Japan</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para TextBreak="No">We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.</Para></Abstract><KeywordGroup Language="En"><Heading>Key words</Heading><Keyword>Parabolic geometry</Keyword><Keyword>simple graded Lie algebras</Keyword><Keyword>Differential equations of finite type</Keyword><Keyword>Contact equivalence</Keyword></KeywordGroup></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Parabolic Geometries Associated with Differential Equations of Finite Type</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Parabolic Geometries Associated with Differential Equations of Finite Type</title></titleInfo><name type="personal"><namePart type="given">Keizo</namePart><namePart type="family">Yamaguchi</namePart><affiliation>Department of Mathematics, Graduate School of Science, Hokkaido University, 060-0810, Sapporo, Japan</affiliation><affiliation>E-mail: yamaguch@math.sci.hokudai.ac.jp</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Tomoaki</namePart><namePart type="family">Yatsui</namePart><affiliation>Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, 070-8621, Asahikawa, Japan</affiliation><affiliation>E-mail: tomoaki@asa.hokkyodai.ac.jp</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="research-article" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Birkhäuser Boston</publisher><place><placeTerm type="text">Boston, MA</placeTerm></place><dateIssued encoding="w3cdtf">2007</dateIssued><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We present here classes of parabolic geometries arising naturally from Se-ashi’s principle to form good classes of linear differential equations of finite type, which generalize the cases of second and third order ODE for scalar functions. We will explicitly describe the symbols of these differential equations. The model equations of these classes admit nonlinear contact transformations and their symmetry algebras become finite dimensional and simple.</abstract><relatedItem type="host"><titleInfo><title>From Geometry to Quantum Mechanics</title><subTitle>In Honor of Hideki Omori</subTitle></titleInfo><name type="personal"><namePart type="given">Yoshiaki</namePart><namePart type="family">Maeda</namePart><affiliation>Department of Mathematics, Faculty of Science and Technology, Keio University, 223-8522, Hiyoshi, Yokohama, Japan</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Takushiro</namePart><namePart type="family">Ochiai</namePart><affiliation>Department of Natural Science, Nippon Sports Science University, 7-1-1, Fukazawa, Setagaya-ku, 158-8508, Tokyo, Japan</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Peter</namePart><namePart type="family">Michor</namePart><affiliation>Facultät für Mathematik, Universität Wein, Nordbergstrasse 15, A-1090, Wein, Austria</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Akira</namePart><namePart type="family">Yoshioka</namePart><affiliation>Department of Mathematics, Tokyo University of Science, 102-8601, Kagurazaka, Tokyo, Japan</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" displayLabel="Contributed volume" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM21022">Differential Geometry</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM21006">Geometry</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM12007">Analysis</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11132">Topological Groups, Lie Groups</topic><topic authority="SpringerSubjectCodes" authorityURI="SCP19013">Mathematical Methods in Physics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCP19080">Quantum Physics</topic></subject><identifier type="DOI">10.1007/978-0-8176-4530-4</identifier><identifier type="ISBN">978-0-8176-4512-0</identifier><identifier type="eISBN">978-0-8176-4530-4</identifier><identifier type="BookTitleID">116157</identifier><identifier type="BookID">978-0-8176-4530-4</identifier><identifier type="BookChapterCount">16</identifier><identifier type="BookVolumeNumber">252</identifier><identifier type="BookSequenceNumber">252</identifier><identifier type="PartChapterCount">5</identifier><part><date>2007</date><detail type="part"><title>Part III: Symplectic Geometry and Poisson Geometry</title></detail><detail type="volume"><number>252</number><caption>vol.</caption></detail><extent unit="pages"><start>161</start><end>209</end></extent></part><recordInfo><recordOrigin>Birkhäuser Boston, 2007</recordOrigin></recordInfo></relatedItem><relatedItem type="series"><titleInfo><title>Progress in Mathematics</title></titleInfo><name type="personal"><namePart type="given">Hyman</namePart><namePart type="family">Bass</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Joseph</namePart><namePart type="family">Oesterlé</namePart><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Alan</namePart><namePart type="family">Weinstein</namePart></name><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>serial</issuance></originInfo><identifier type="SeriesID">4848</identifier><part><detail type="volume"><number>Part III</number><caption>vol.</caption></detail></part><recordInfo><recordOrigin>Birkhäuser Boston, 2007</recordOrigin></recordInfo></relatedItem><identifier type="istex">0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816</identifier><identifier type="ark">ark:/67375/HCB-XH40HZCT-P</identifier><identifier type="DOI">10.1007/978-0-8176-4530-4_11</identifier><identifier type="ChapterID">11</identifier><identifier type="ChapterID">Chap11</identifier><accessCondition type="use and reproduction" contentType="copyright">Birkhäuser Boston, 2007</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Birkhäuser Boston, 2007</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/metadata/json</uri></json:item></metadata><annexes><json:item><extension>txt</extension><original>true</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816/annexes/txt</uri></json:item></annexes></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000325 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000325 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:0F0359A8FB3EA56D944AA256EAE4EA4AD05CB816
|texte= Parabolic Geometries Associated with Differential Equations of Finite Type
}}
| This area was generated with Dilib version V0.6.33. |  |