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The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds
Інший ID:
2010 Mathematics Subject Classification: 53C30; 53C15; 53C07
DOI: http://dx.doi.org/10.3842/SIGMA.2013.074
DOI: http://dx.doi.org/10.3842/SIGMA.2013.074
Посилання:
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.
Підтримка:
The author acknowledges many helpful discussions with Erc¨ument Orta¸cgil.
Дата:
2013
Переглядів:
467
Завантажень:
231
Анотація:
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.
