NON-REDUCTIVE HOMOGENEOUS 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/10.52065/2520-6141-2024-278-1.

 

Key words: equiaffine connection, homogeneous space, Ricci tensor, reductive space, torsion tensor

For citation: : Mozhey N. P. Non-reductive homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2024, no. 1 (278), pp. 5–10 (In Russian). DOI: 10.52065/2520-6141-2024-278-1.

Abstract

The purpose of this paper is to describe three-dimensional non-reductive homogeneous spaces that do not admit equiaffine connections, the case of an unsolvable Lie group of transformations is considered. The basic notions, such as an isotropically-faithful pair, a reductive space, an affine connection, a torsion tensor, a curvature tensor, Ricci tensor, an equiaffine (locally equiaffine) connection, are defined. Studies are based on the application of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character. The peculiarity of techniques presented in the work is the use of purely algebraic approach to the description of manifolds and connections on them, as well as compound of methods of differential geometry, the theory of Lie groups and algebras and the theory of homogeneous spaces. The results obtained can be used in the study of manifolds, as well as have applications in variousfields of mathematics and physics, since many fundamental problems in these fields are connected with the study of invariant objects on homogeneous spaces.

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15.11.2023