SYMMETRIC SPACES OF UNSOLVABLE LIE GROUPS THAT DO NOT ADMIT EQUIAFFINE CONNECTIONS

UDC 514.76

  • Mozhey Natalya Pavlovna – PhD (Physics and Mathematics), Associate Professor, Assistant Professor, the Department of Software for Information Technologies. Belarusian State University of Informatics and Radioelectronics (6, P. Brovki str., 220013, Minsk, Republic of Belarus). E-mail: mozheynatalya@mail.ru

DOI: https://doi.org/10.52065/2520-6141-2023-266-1-4

Keywords: equiaffine connection, transformation group, symmetric space, torsion tensor.

For citation: Mozhey N. P. Symmetric spaces of unsolvable Lie groups that do not admit equiaffine connections. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2023, no. 1 (266), pp. 20–23. DOI: https://doi.org/10.52065/2520-6141-2023-266-1-4.

Abstract

The paper considers three-dimensional symmetric homogeneous spaces on which an unsolvable group of transformations with an unsolvable stabilizer acts. The purpose of this work is to describe all such spaces that do not admit invariant equiaffine connections. The basic notions, such as isotropicallyfaithful pair, symmetric space, canonical decomposition, affine connection, curvature and torsion tensors, Ricci tensor, equiaffine connection are defined. In the main part of the work for three-dimensional symmetric homogeneous spaces of unsolvable Lie groups, it is determined under what conditions the space does not admit equiaffine connections. The results can be used in the study of manifolds, as well as have applications in various fields of mathematics and physics, since many fundamental problems in these fields are connected with the study of in-variant objects on homogeneous spaces. Studies are based on the application of properties of the homogeneous spaces and structures on them and they mainly have local character. The peculiarity of presented techniques is the use of purely algebraic approach to the description of manifolds and connections on them.

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27.12.2022