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Article

Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces

1
Department of Mathematics and Physics, Uman National University of Horticulture, 20300 Uman, Ukraine
2
Department of Physics and Mathematics Sciences, Odesa National Academy of Food Technologies, 65039 Odesa, Ukraine
3
Institute of Mathematics and Descriptive Geometry, Brno University of Technology, 60200 Brno, Czech Republic
4
Department of Algebra and Geometry, Palacký University Olomouc, 77147 Olomouc, Czech Republic
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1560; https://doi.org/10.3390/math8091560
Received: 28 July 2020 / Revised: 7 September 2020 / Accepted: 8 September 2020 / Published: 11 September 2020
(This article belongs to the Special Issue Differential Geometry of Spaces with Structures)
In the paper, we consider geodesic mappings of spaces with an affine connections onto generalized symmetric and Ricci-symmetric spaces. In particular, we studied in detail geodesic mappings of spaces with an affine connections onto 2-, 3-, and m- (Ricci-) symmetric spaces. These spaces play an important role in the General Theory of Relativity. The main results we obtained were generalized to a case of geodesic mappings of spaces with an affine connection onto (Ricci-) symmetric spaces. The main equations of the mappings were obtained as closed mixed systems of PDEs of the Cauchy type in covariant form. For the systems, we have found the maximum number of essential parameters which the solutions depend on. Any m- (Ricci-) symmetric spaces (m1) are geodesically mapped onto many spaces with an affine connection. We can call these spaces projectivelly m- (Ricci-) symmetric spaces and for them there exist above-mentioned nontrivial solutions. View Full-Text
Keywords: geodesic mapping; space with an affine connection; m-symmetric space; m-Ricci-symmetric space geodesic mapping; space with an affine connection; m-symmetric space; m-Ricci-symmetric space
MDPI and ACS Style

Berezovski, V.; Cherevko, Y.; Hinterleitner, I.; Peška, P. Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces. Mathematics 2020, 8, 1560. https://doi.org/10.3390/math8091560

AMA Style

Berezovski V, Cherevko Y, Hinterleitner I, Peška P. Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces. Mathematics. 2020; 8(9):1560. https://doi.org/10.3390/math8091560

Chicago/Turabian Style

Berezovski, Volodymyr, Yevhen Cherevko, Irena Hinterleitner, and Patrik Peška. 2020. "Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces" Mathematics 8, no. 9: 1560. https://doi.org/10.3390/math8091560

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