Fundamental Theorems for Timelike Surfaces in the Minkowski 4-Space
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910362138312704 |
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| author | Bencheva, Victoria Milousheva, Velichka |
| author_facet | Bencheva, Victoria Milousheva, Velichka |
| contents | In the present paper, we study timelike surfaces free of minimal points in the four-dimensional Minkowski space. For each such surface we introduce a geometrically determined pseudo-orthonormal frame field and writing the derivative formulas with respect to this moving frame field and using the integrability conditions, we obtain a system of six functions satisfying some natural conditions. In the general case, we prove a Fundamental Bonnet-type theorem (existence and uniqueness theorem) stating that these six functions, satisfying the natural conditions, determine the surface up to a motion. In some particular cases, we reduce the number of functions and give the fundamental theorems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_06721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fundamental Theorems for Timelike Surfaces in the Minkowski 4-Space Bencheva, Victoria Milousheva, Velichka Differential Geometry 53B30, 53A35, 53B25 In the present paper, we study timelike surfaces free of minimal points in the four-dimensional Minkowski space. For each such surface we introduce a geometrically determined pseudo-orthonormal frame field and writing the derivative formulas with respect to this moving frame field and using the integrability conditions, we obtain a system of six functions satisfying some natural conditions. In the general case, we prove a Fundamental Bonnet-type theorem (existence and uniqueness theorem) stating that these six functions, satisfying the natural conditions, determine the surface up to a motion. In some particular cases, we reduce the number of functions and give the fundamental theorems. |
| title | Fundamental Theorems for Timelike Surfaces in the Minkowski 4-Space |
| topic | Differential Geometry 53B30, 53A35, 53B25 |
| url | https://arxiv.org/abs/2403.06721 |