Lie transformation groups and geometry. (English) Zbl 1205.53054

Arvanitoyeorgos, Andreas

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 11-35 (2008).

Summary: We present geometrical aspects of Lie groups and reductive homogeneous spaces, and some recent results on homogeneous geodesics and homogeneous Einstein metrics. The article is based on the four lectures given at the ninth international conference on Geometry, Integrability and Quantization, June 8–13, 2007, Varna, Bulgaria.
Contents: 1. Introduction; 2. Lie groups; 3. Homogeneous spaces; 4. Geometry of compact Lie groups and homogeneous spaces; 5. Homogeneous Einstein metrics; References.
For the entire collection see [Zbl 1154.17001].

MSC:

53C30

Differential geometry of homogeneous manifolds

Keywords:

reductive homogeneous spaces; homogeneous geodesics; Einstein metrics