Timelike Surfaces with Parallel Normalized Mean Curvature Vector Field in the Minkowski 4-Space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910299676737536 |
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| author | Bencheva, Victoria Milousheva, Velichka |
| author_facet | Bencheva, Victoria Milousheva, Velichka |
| contents | In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge problem for this class of surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Timelike Surfaces with Parallel Normalized Mean Curvature Vector Field in the Minkowski 4-Space Bencheva, Victoria Milousheva, Velichka Differential Geometry 53B30, 53A35, 53B25 In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge problem for this class of surfaces. |
| title | Timelike Surfaces with Parallel Normalized Mean Curvature Vector Field in the Minkowski 4-Space |
| topic | Differential Geometry 53B30, 53A35, 53B25 |
| url | https://arxiv.org/abs/2401.09024 |