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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149366 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862720565794570240 |
|---|---|
| author | Blaom, A.D. |
| author_facet | Blaom, A.D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T18:26:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149366 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:26:29Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Blaom, A.D. 2019-02-21T07:22:22Z 2019-02-21T07:22:22Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/149366 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. The author acknowledges many helpful discussions with Erc¨ument Orta¸cgil. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds Article published earlier |
| spellingShingle | The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds Blaom, A.D. |
| title | 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_short | The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds |
| title_sort | infinitesimalization and reconstruction of locally homogeneous manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149366 |
| work_keys_str_mv | AT blaomad theinfinitesimalizationandreconstructionoflocallyhomogeneousmanifolds AT blaomad infinitesimalizationandreconstructionoflocallyhomogeneousmanifolds |