The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
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 ex...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149366 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |