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On Geodesic Definiteness by Similarity Points

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Abstract

In this paper, we present some results obtained in the theory of geodesic mappings of surfaces. It is well known that a mapping that is both conformal and geodesic is homothetic. Based on this property, we obtain new results on the definiteness of surfaces with respect to geodesic mappings, which generalize results obtained by V. T. Fomenko.

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Authors and Affiliations

  1. Brno University of Technology, Brno, Czech Republic

    I. Hinterleitner

  2. Moscow Pedagogical State University, Moscow, Russia

    N. I. Guseva

  3. Russian Institute for Scientific and Technical Information of the Russian Academy of Sciences, Moscow, Russia

    N. I. Guseva

  4. Palacký University Olomouc, Olomouc, Czech Republic

    J. Mikeš

Authors
  1. I. Hinterleitner
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  2. N. I. Guseva
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  3. J. Mikeš
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Correspondence to I. Hinterleitner.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 182, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor V. T. Bazylev. Moscow, April 22-25, 2019. Part 4, 2020.

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Hinterleitner, I., Guseva, N.I. & Mikeš, J. On Geodesic Definiteness by Similarity Points. J Math Sci 277, 727–735 (2023). https://doi.org/10.1007/s10958-023-06879-z

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