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

Author

Listed:
  • Volodymyr Berezovski

    (Department of Mathematics and Physics, Uman National University of Horticulture, 20300 Uman, Ukraine)

  • Yevhen Cherevko

    (Department of Physics and Mathematics Sciences, Odesa National Academy of Food Technologies, 65039 Odesa, Ukraine)

  • Irena Hinterleitner

    (Institute of Mathematics and Descriptive Geometry, Brno University of Technology, 60200 Brno, Czech Republic)

  • Patrik Peška

    (Department of Algebra and Geometry, Palacký University Olomouc, 77147 Olomouc, Czech Republic)

Abstract

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 ( m ≥ 1 ) 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.

Suggested Citation

  • Volodymyr Berezovski & Yevhen Cherevko & Irena Hinterleitner & Patrik Peška, 2020. "Geodesic Mappings of Spaces with Affine Connections onto Generalized Symmetric and Ricci-Symmetric Spaces," Mathematics, MDPI, vol. 8(9), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1560-:d:412027
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    References listed on IDEAS

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    1. Volodymyr Berezovski & Yevhen Cherevko & Lenka Rýparová, 2019. "Conformal and Geodesic Mappings onto Some Special Spaces," Mathematics, MDPI, vol. 7(8), pages 1-8, July.
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    Cited by:

    1. Igor G. Shandra & Josef Mikeš, 2022. "Geodesic Mappings of Semi-Riemannian Manifolds with a Degenerate Metric," Mathematics, MDPI, vol. 10(1), pages 1-11, January.
    2. Nenad O. Vesić & Dušan J. Simjanović & Branislav M. Randjelović, 2024. "Invariants for Second Type Almost Geodesic Mappings of Symmetric Affine Connection Space," Mathematics, MDPI, vol. 12(15), pages 1-15, July.

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    2. Volodymyr Berezovski & Yevhen Cherevko & Irena Hinterleitner & Patrik Peška, 2022. "Geodesic Mappings onto Generalized m -Ricci-Symmetric Spaces," Mathematics, MDPI, vol. 10(13), pages 1-12, June.

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