On geometry on a two-dimensional plane in a five-dimensional pseudo-Euclidean space of index two
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
EDP Sciences
2024-01-01
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| Series: | E3S Web of Conferences |
| Online Access: | https://www.e3s-conferences.org/articles/e3sconf/pdf/2024/117/e3sconf_greenenergy24_01025.pdf |
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| Summary: | 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. |
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| ISSN: | 2267-1242 |