NORMAL CONNECTIONS ON REDUCTIVE HOMOGENEOUS SPACES WITH AN UNSOLVABLE TRANSFORMATION GROUP
Abstract
In this article we present the local classification of three-dimensional reductive homogeneous spaces allowing a normal connection. We consider the case, when the Lie group of transformations is unsolvable and the stabilizer is usolvable too. We describe all invariant affine connections together with their curvature and torsion tensors, canonical connections and natural torsion-free connections. We study the holonomy algebras of homogeneous spaces, and sind when the invariant connection is normal.
About the Author
N. P. Mozhey
Belarusian State University of Informatics and Radioelectronics
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor, Department of Software Information Technology
Belarus
Ph. D. (Physics and Mathematics), Assistant Professor, Department of Software Information Technology
References
1. Kobayashi Sh., Nomizu K. Foundations of differential geometry. New York, Interscience Publishers, 1963.
2. Kartan E. Riemannian geometry in an orthogonal frame. Moscow, Moscow University Publ., 1960. 307 p. (in Russian)
3. Chen B. Y. Geometry of submanifolds. New York, Dekker, 1973. 308 p.
4. Onishchik A. L. Topology of transitive transformation groups. Moscow, Fizmatlit Publishing Company, 1995. 384 p. (in Russian)
5. Nomizu K. Invariant affine connections on homogeneous spaces. American Journal of Mathematics, 1954, vol. 76, no. 1, pp. 33–65. doi: 10.2307/2372398.
6. Mozhey N. P. Three-dimensional isotropically-faithful homogeneous spaces and connections on it. Kazan, Publisher University of Kazan, 2015. 394 p. (in Russian)
7. Mozhey N. P. Normal Connections on Three-Dimensional Homogeneous Spaces with a NonSolvable Transformation Group. I. A Non-Solvable Stabilizer. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki [Proceedings of Kazan University. Physics and Mathematics Series], 2013, vol. 155, book 4, pp. 61–76. (in Russian)
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