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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149366 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149366 |
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irk-123456789-1493662019-02-22T01:23:28Z The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds Blaom, A.D. 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. 2013 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Blaom, A.D. |
| spellingShingle |
Blaom, A.D. The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Blaom, A.D. |
| author_sort |
Blaom, A.D. |
| title |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_short |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_full |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_fullStr |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_full_unstemmed |
The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_sort |
infinitesimalization and reconstruction of locally homogeneous manifolds |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149366 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT blaomad theinfinitesimalizationandreconstructionoflocallyhomogeneousmanifolds AT blaomad infinitesimalizationandreconstructionoflocallyhomogeneousmanifolds |
| first_indexed |
2023-05-20T17:32:50Z |
| last_indexed |
2023-05-20T17:32:50Z |
| _version_ |
1796153537438154752 |