Issue |
E3S Web Conf.
Volume 587, 2024
International Scientific Conference on Green Energy (GreenEnergy 2024)
|
|
---|---|---|
Article Number | 01025 | |
Number of page(s) | 9 | |
Section | Energy Production, Transmission, Distribution and Storage | |
DOI | https://doi.org/10.1051/e3sconf/202458701025 | |
Published online | 07 November 2024 |
On geometry on a two-dimensional plane in a five-dimensional pseudo-Euclidean space of index two
1 Fergana State University, Fergana 150100, Uzbekistan
2 Urgench state University, Urgench 220100, Uzbekistan
3 Tashkent State Transport University, Tashkent 100002 Uzbekistan
* Corresponding author: bm.mamadaliyev@pf.fdu.uz
The study of the geometry of surfaces having a codimension greater than one in multidimensional spaces is one of the most difficult problems in geometry. When the multidimensional geometry under consideration has a pseudo-Euclidean metric, its complexity increases. Two-dimensional surfaces in a five-dimensional pseudo-Euclidean space of index two are considered in the article. Geometry on two-dimensional planes of this space can be of three types, Euclidean, Minkowski, and Galilean. Therefore, two-dimensional surfaces are also divided into three types according to the geometry on the tangent plane. A special class of two-dimensional surfaces given by a vector equation is considered. Using the dual space, the geometry of a two-dimensional surface is studied, reduced to a Euclidean or pseudo-Euclidean surface of a three-dimensional space. Conditions are revealed and theorems are proved on the existence of a surface that does not lie in a four-dimensional hyperplane and has tangent planes with one internal geometry.
© The Authors, published by EDP Sciences, 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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