Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914594823340032 |
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| author | Kassabov, Ognian |
| author_facet | Kassabov, Ognian |
| contents | The geometrically defined wide class of time-like surfaces in $\mathbb R^3$, admitting real asymptotic lines is considered. A fundamental theorem of Bonnet-type is obtained for these surfaces. It states that a surface in this class is determined (up to a motion) by four invariant functions, satisfying some natural PDEs. Then canonical parameters are defined for these surfaces and it is proved that such a surface is determined (up to a motion) in canonical parameters with only two invariant functions (which in particular can be the Gauss and the mean curvature), satisfying a partial differential equation, equivalent to the Gauss equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24444 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines Kassabov, Ognian Differential Geometry The geometrically defined wide class of time-like surfaces in $\mathbb R^3$, admitting real asymptotic lines is considered. A fundamental theorem of Bonnet-type is obtained for these surfaces. It states that a surface in this class is determined (up to a motion) by four invariant functions, satisfying some natural PDEs. Then canonical parameters are defined for these surfaces and it is proved that such a surface is determined (up to a motion) in canonical parameters with only two invariant functions (which in particular can be the Gauss and the mean curvature), satisfying a partial differential equation, equivalent to the Gauss equation. |
| title | Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.24444 |