Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines

Ognian Kassabov

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arXiv · 2605.24444

Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines

Ognian Kassabov

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Abstract

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.

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BibTeX RIS

Ognian Kassabov. 2026-05-23. Basic invariants for time-like surfaces in $\mathbb R^3_1$ with real asymptotic lines. https://arxiv.org/abs/2605.24444

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