Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

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Володимир Анатолійович Кіосак
Олександр Олегович Пришляк
https://orcid.org/0000-0002-7164-807X
Олександр Васильович Лесечко
https://orcid.org/0000-0002-2352-6174

Abstract

The paper treats two pseudo-Riemannian spaces having common geodesic lines. Certain algebraic and differential conditions are imposed on the Riemann tensor of one of the spaces, while an operation of lowering indices and a calculation of the covariant derivative is carried out with respect to metrics and connection objects of the another space. In order to study the objects we introduce a special supplementary tensor. It is proven that, when the additional conditions are true, then either the spaces do not admit non-trivial mappings or the spaces are equidistant spaces. We apply tensor methods without limitations imposed on the sign of the metric under question.

Keywords:
pseudo-Riemannian spaces, geodesic mapping, supplementary tensor

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How to Cite
Кіосак, В., Пришляк, О., & Лесечко, О. (2021). On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor. Proceedings of the International Geometry Center, 14(4), 13-26. https://doi.org/10.15673/tmgc.v14i4.2140
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Papers

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