Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 28–41. ISSN 2079-6641

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MSC 53A15, 53A55, 53B30

Research Article

Equivalence of paths in some non-Euclidean geometry

R. A. Gafforov¹, K. K. Muminov²

¹Fergana State University, 150100, Fergana, st. Murabbiylar, 19, Republic of Uzbekistan
²National University of Uzbekistan, 100174, Tashkent, Mirzo Ulugbek str., Republic of Uzbekistan
E-mail: gafforov.rahmatjon@mail.ru

Let G be a subgroup of the group of all reversible linear transformations of a finitedimensional real space Rn. One of the problems of differential geometry is to find easily verifiable necessary and sufficient conditions that ensure that G is the equivalence of paths lying in Rn. The article establishes the necessary and sufficient conditions for the equivalence of paths in some non-Euclidean geometry.

Key words: pseugo-Galilean space, group of movements, regular path.

DOI: 10.26117/2079-6641-2022-40-3-28-41

Original article submitted: 22.09.2022

Revision submitted: 22.10.2022

For citation. Gafforov R. A., Muminov K. K. Equivalence of paths in some non-Euclidean geometry. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 28-41. DOI: 10.26117/2079-6641-2022-40-3-28-41

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)

© Gafforov R. A., Muminov K. K., 2022

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Gafforov Rahmatjon Abdukaxxorovich – Teacher of the Faculty of mathematics and informatics Fergana State University, Fergana, Republic of Uzbekistan, ORCID 0000-0002-4589-5421.

Muminov Kobiljon Kodirovich – D. Sci. (Phys. & Math.), Professor, Faculty of Mechanics and Mathematics, National University of Uzbekistan, Tashkent, Republic of Uzbekistan, ORCID 0000-0002-2445-749X.

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