The Infinitesimalization and Reconstruction of Locally Homogeneous Manifolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Author: Blaom, A.D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149366
• 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.

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...