THREE-DIMENSIONAL REDUCTIVE HOMOGENEOUS SPACES OF UNSOLVABLE LIE GROUPS
Abstract
In this article we present a local classification of three-dimensional reductive homogeneous spaces allowing a normal connection. We have concerned the case of the unsolvable Lie group of transformations with a solvable stabilizer. We describe all invariant affine connections together with their curvature and torsion tensors, canonical connections and natural torsion-free connections. We have studied the holonomy algebras of homogeneous spaces and have found when the invariant connection is normal.
About the Author
N. P. Mozhey
Belarusian State University of Informatics and Radioelectronics
Russian Federation
Russian Federation
References
1. Kobayashi Sh., Nomizu K. Foundations of differential geometry. New York, Interscience Publishers, 1963.
2. Onishchik A. L. Topology of transitive transformation groups. Moscow, Fizmatlit Publ., 1995. 384 p. (in Russian)
3. Mozhey N. P. Three-dimensional isotropically-faithful homogeneous spaces and connections on them. Kazan, Publisher University of Kazan, 2015. 394 p. (in Russian)
4. Mozhey N. P. Normal Connections on Three-Dimensional Homogeneous Spaces with a Non-Solvable Transformation Group. II. A Solvable Stabilizer. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki [Proceedings of Kazan University. Physics and Mathematics Series], 2014, vol. 156, pp. 51–70. (in Russian)
5. Nomizu K. Invariant affine connections on homogeneous spaces. American Journal of Mathematics, 1954, vol. 76, no. 1, pp. 33–65. doi.org/10.2307/2372398.
Review
Views: 1238
Email this article 