GEOMETRY IN SEMI-EUCLIDEAN SPACES
DOI:
https://doi.org/10.52754/16948645_2023_1_29Keywords:
An isotropic space, Gallеan space, isotropic sphere, first and second fundamental form, An isotropic space, Gallеan space, isotropic sphere, first and second fundamental formAbstract
The geometry of semi-Euclidean spaces is an intensively developed part of non-Euclidean geometry. The paper presents the main results obtained over the past thirty years on the geometry of three-dimensional semi-Euclidean spaces. Three-dimensional semi-Euclidean spaces are isotropic and Galilean spaces. At the end of the paper, several unsolved problems in the Galilean and isotropic space are presented.
References
Artykbaev A. The dual surfaces of an isotropic space [Text] / A. Artykbaev, Sh. Ismoilov. – Bull. Inst. Math., 2021, Vol-4, Issue-4, pp. 1-8.
Артыкбаев А. Геометрия в целом в пространстве время[Teкст] / А. Артыкбаев, Д.Д. Соколов. – Ташкент, Фан, 1991, 120-127 c.
Artykbaev A. Special mean and total curvature of a dual surface in isotropic spaces[Text] / A. Artykbaev, Sh. Ismoilov. – International electronic journal of geometry, 2022, volume 15, Issue 1, pp. 1–10. DOI: https://doi.org/10.36890/iejg.972370
Artykbaev A. Surface recovering by a give total and mean curvature in isotropic space [Text] / A. Artykbaev, Sh.Ismoilov. – Palestine Journal of Mathematics, 2022, vol-11(3), pp. 351-361.
Aydin M.E.Affine factorable surfaces in isotropic spaces[Text] / M.E. Aydin, A.E Kara, V. Ergüt. – TWMS J. Pure Appl. Math., 2020, Vol-11, N-1, pp.72-88.
Aydin M. E. Translation hypersurfaces with constant curvature in 4-dimensional isotropic space[Text] / M. E. Aydin, A.O. Ogrenmis. – International Journal of Maps in Mathematics, 2019, Vol-2, Issue 1, pp. 108-130.
Розенфельд Б. А. Неевклидовы геометрии[Teкст]/ Б. А. Розенфельд, Москва Наука, 1969, 547 с.
Sachs H. Isotrop Geometri des Raumes[Text] / H.Sachs. – 1990 -300 c. DOI: https://doi.org/10.1007/978-3-322-83785-1
Lone M.S. Dual translation surfaces in the three dimensional simply isotropic space [Text] / M.S. Lone, M.K. Karacan. – Tamkang journal of mathematics, 2018, Volume 49, Number 1, 67-77. DOI: https://doi.org/10.5556/j.tkjm.49.2018.2476
Karacan M. K., Yoon D. W. and Bukcu B., Translation surfaces in the three-dimensional simply isotropic space [Text] / M. K. Karacan, D. W. Yoon, B. Bukcu – Int. J. Geom. Methods Mod. Phys., 2016, Vol-13(7). DOI: https://doi.org/10.1142/S0219887816500882
Strubecker K. Differential geometrie des isotropen Raumes I,II III [Text] / K. Strubecker, – Math.Z. 1942, vol-47, 743-777; 1942, vol-48 369-427; 1943, vol-48 369-427. DOI: https://doi.org/10.1007/BF01180022
Ismoilov Sh.Sh. Geometry of the Monge - Ampere equation in an isotropic space [Text] / Sh.Sh. Ismoilov, – Uzbek Mathematical Journal, 2022, vol-66, issue-2, pp. 66-77. DOI: https://doi.org/10.29229/uzmj.2022-2-7
Ismoilov Sh.Sh. Cyclic surfaces in pseudo-euclidean space[Text] / Sh.Sh. Ismoilov, B.M. Sultanov., – India, International Journal of Statistics and Applied Mathematics. 2020. Volume 5, №1, pp. 28-31.
Султанов Б.М. Существование циклической поверхности по заданной функции полной кривизны[Teкст] /Б.М. Султанов, – Вестник НУУ. 2017, №22, стр. 201- 204.
Исмоилов Ш.Ш. Свойства двойственной поверхности в многомерном изотропном пространстве[Teкст]/ Ш.Ш. Исмоилов,–– Tashkent, Physical and mathematical sciences, 2022. Volume 3. Issue 1. – P. 47-58
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Journal of Osh State University. Mathematics. Physics. Technical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
