On low-dimensional manifolds with isometric SO0( p, q )-actions
Identifieur interne : 000158 ( Main/Exploration ); précédent : 000157; suivant : 000159On low-dimensional manifolds with isometric SO0( p, q )-actions
Auteurs : Gestur Lafsson [États-Unis] ; Raul Quiroga-Barranco [Mexique]Source :
- Transformation Groups [ 1083-4362 ] ; 2012-09-01.
Abstract
Abstract: Let G be a non-compact simple Lie group with Lie algebra $ \mathfrak{g} $ . Denote with m( $ \mathfrak{g} $ ) the dimension of the smallest non-trivial $ \mathfrak{g} $ -module with an invariant non-degenerate symmetric bilinear form. For an irreducible finite volume pseudo-Riemannian analytic manifold M it is observed that dim(M) ≥ dim(G) + m( $ \mathfrak{g} $ ) when M admits an isometric G-action with a dense orbit. The Main Theorem considers the case $ G = {\widetilde {\text{SO}}_0}\left( {p,q} \right) $ , providing an explicit description of M when the bound is achieved. In such a case, M is (up to a finite covering) the quotient by a lattice of either $ {\widetilde {\text{SO}}_0}\left( {p + 1,q} \right) $ or $ {\widetilde {\text{SO}}_0}\left( {p,q + 1} \right) $ .
Url:
DOI: 10.1007/s00031-012-9194-5
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002A58
- to stream Istex, to step Curation: 002A58
- to stream Istex, to step Checkpoint: 000124
- to stream Main, to step Merge: 000158
- to stream Main, to step Curation: 000158
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On low-dimensional manifolds with isometric SO0( p, q )-actions</title>
<author><name sortKey=" Lafsson, Gestur" sort=" Lafsson, Gestur" uniqKey=" Lafsson G" first="Gestur" last=" Lafsson">Gestur Lafsson</name>
</author>
<author><name sortKey="Quiroga Barranco, Raul" sort="Quiroga Barranco, Raul" uniqKey="Quiroga Barranco R" first="Raul" last="Quiroga-Barranco">Raul Quiroga-Barranco</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:CE913EC8805283482450C39C2C145EE4A220BF06</idno>
<date when="2012" year="2012">2012</date>
<idno type="doi">10.1007/s00031-012-9194-5</idno>
<idno type="url">https://api.istex.fr/document/CE913EC8805283482450C39C2C145EE4A220BF06/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">002A58</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002A58</idno>
<idno type="wicri:Area/Istex/Curation">002A58</idno>
<idno type="wicri:Area/Istex/Checkpoint">000124</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000124</idno>
<idno type="wicri:doubleKey">1083-4362:2012: Lafsson G:on:low:dimensional</idno>
<idno type="wicri:Area/Main/Merge">000158</idno>
<idno type="wicri:Area/Main/Curation">000158</idno>
<idno type="wicri:Area/Main/Exploration">000158</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On low-dimensional manifolds with isometric SO0( p, q )-actions</title>
<author><name sortKey=" Lafsson, Gestur" sort=" Lafsson, Gestur" uniqKey=" Lafsson G" first="Gestur" last=" Lafsson">Gestur Lafsson</name>
<affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country>
<wicri:regionArea>Department of Mathematics, 322 Lockett Hall, Louisiana State University, 70803, Baton Rouge, LA</wicri:regionArea>
<placeName><region type="state">Louisiane</region>
</placeName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country>
</affiliation>
</author>
<author><name sortKey="Quiroga Barranco, Raul" sort="Quiroga Barranco, Raul" uniqKey="Quiroga Barranco R" first="Raul" last="Quiroga-Barranco">Raul Quiroga-Barranco</name>
<affiliation wicri:level="1"><country xml:lang="fr">Mexique</country>
<wicri:regionArea>Centro de Investigación en Matemáticas, Guanajuato, Apartado Postal 402, 36000, Guanajuato</wicri:regionArea>
<wicri:noRegion>Guanajuato</wicri:noRegion>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Mexique</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j">Transformation Groups</title>
<title level="j" type="abbrev">Transformation Groups</title>
<idno type="ISSN">1083-4362</idno>
<idno type="eISSN">1531-586X</idno>
<imprint><publisher>SP Birkhäuser Verlag Boston</publisher>
<pubPlace>Boston</pubPlace>
<date type="published" when="2012-09-01">2012-09-01</date>
<biblScope unit="volume">17</biblScope>
<biblScope unit="issue">3</biblScope>
<biblScope unit="page" from="835">835</biblScope>
<biblScope unit="page" to="860">860</biblScope>
</imprint>
<idno type="ISSN">1083-4362</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">1083-4362</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Abstract: Let G be a non-compact simple Lie group with Lie algebra $ \mathfrak{g} $ . Denote with m( $ \mathfrak{g} $ ) the dimension of the smallest non-trivial $ \mathfrak{g} $ -module with an invariant non-degenerate symmetric bilinear form. For an irreducible finite volume pseudo-Riemannian analytic manifold M it is observed that dim(M) ≥ dim(G) + m( $ \mathfrak{g} $ ) when M admits an isometric G-action with a dense orbit. The Main Theorem considers the case $ G = {\widetilde {\text{SO}}_0}\left( {p,q} \right) $ , providing an explicit description of M when the bound is achieved. In such a case, M is (up to a finite covering) the quotient by a lattice of either $ {\widetilde {\text{SO}}_0}\left( {p + 1,q} \right) $ or $ {\widetilde {\text{SO}}_0}\left( {p,q + 1} \right) $ .</div>
</front>
</TEI>
<affiliations><list><country><li>Mexique</li>
<li>États-Unis</li>
</country>
<region><li>Louisiane</li>
</region>
</list>
<tree><country name="États-Unis"><region name="Louisiane"><name sortKey=" Lafsson, Gestur" sort=" Lafsson, Gestur" uniqKey=" Lafsson G" first="Gestur" last=" Lafsson">Gestur Lafsson</name>
</region>
<name sortKey=" Lafsson, Gestur" sort=" Lafsson, Gestur" uniqKey=" Lafsson G" first="Gestur" last=" Lafsson">Gestur Lafsson</name>
</country>
<country name="Mexique"><noRegion><name sortKey="Quiroga Barranco, Raul" sort="Quiroga Barranco, Raul" uniqKey="Quiroga Barranco R" first="Raul" last="Quiroga-Barranco">Raul Quiroga-Barranco</name>
</noRegion>
<name sortKey="Quiroga Barranco, Raul" sort="Quiroga Barranco, Raul" uniqKey="Quiroga Barranco R" first="Raul" last="Quiroga-Barranco">Raul Quiroga-Barranco</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000158 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000158 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Mathematiques |area= BourbakiV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:CE913EC8805283482450C39C2C145EE4A220BF06 |texte= On low-dimensional manifolds with isometric SO0( p, q )-actions }}
This area was generated with Dilib version V0.6.33. |