The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
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| Creator |
Blaom, A.D.
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| Description |
A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold M is locally homogeneous – i.e., admits an atlas of charts modeled on some homogeneous space G/H – if and only if there exists a transitive Lie algebroid over M admitting a flat Cartan connection that is 'geometrically closed'. It is shown how the torsion and monodromy of the connection determine the particular form of G/H. Under an additional completeness hypothesis, local homogeneity becomes global homogeneity, up to cover.
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| Date |
2019-02-21T07:22:22Z
2019-02-21T07:22:22Z 2013 |
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| Type |
Article
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| Identifier |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds / A.D. Blaom // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 17 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 53C30; 53C15; 53C07 DOI: http://dx.doi.org/10.3842/SIGMA.2013.074 http://dspace.nbuv.gov.ua/handle/123456789/149366 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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