Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On geodesic mappings of symmetric pairs

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Volodymyr Kiosak
https://orcid.org/0000-0002-7433-6709
Olexandr Lesechko
https://orcid.org/0000-0002-2352-6174
Olexandr Latysh
http://orcid.org/0000-0001-8914-2889

Abstract

The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.

Keywords:
symmetric spaces, symmetric pair of spaces, geodesic mappings

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How to Cite
Kiosak, V., Lesechko, O., & Latysh, O. (2023). On geodesic mappings of symmetric pairs. Proceedings of the International Geometry Center, 15(3-4), 230-238. https://doi.org/10.15673/tmgc.v15i3-4.2430
Section
Papers