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Particular Cases of Quasi-Parallelograms of Type I on the Lobachevsky Plane

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Abstract

In this paper, we consider particular cases of quasi-parallelograms, which are obtained by transferring to the Lobachevsky plane various characteristic properties of rhombuses, rectangles, and squares of the Euclidean plane based on their diagonals. The existence of these quadrangles is proved by using the Cayley–Klein model in the circle of the Euclidean plane.

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References

  1. L. S. Atanasyan, Lobachevsky Geometry [in Russian], Prosveshchenie, Moscow (2001).

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  6. M. S. Maskina and M. I. Kuptsov, “Special cases of hyperbolic parallelograms on the Lobachevsky plane,” in: Proc. Int. Conf. “Geometric Methods in Control Theory and Mathematical Physics” [in Russian], Ryazan State Univ., Ryazan (2018), pp. 53–54.

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Authors and Affiliations

  1. Academy of Law Management of the Federal Penal Service of Russia, Ryazan, Russia

    M. S. Maskina & T. A. Zhilnikov

Authors
  1. M. S. Maskina
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  2. T. A. Zhilnikov
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Correspondence to M. S. Maskina.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 181, 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 3, 2020.

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Maskina, M.S., Zhilnikov, T.A. Particular Cases of Quasi-Parallelograms of Type I on the Lobachevsky Plane. J Math Sci 276, 759–766 (2023). https://doi.org/10.1007/s10958-023-06799-y

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  • DOI: https://doi.org/10.1007/s10958-023-06799-y

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