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:
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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)
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