IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1560-d412027.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1560/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1560/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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 1-14, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Volodymyr Berezovski & Josef Mikeš & Lenka Rýparová & Almazbek Sabykanov, 2020. "On Canonical Almost Geodesic Mappings of Type π 2 ( e )," Mathematics, MDPI, vol. 8(1), pages 1-8, January.
    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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1560-:d:412027. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.