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arXiv · 2305.04230

Null surfaces of pseudo-spherical spacelike framed curves in the anti-de Sitter 3-space

O. Ogulcan Tuncer
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Abstract

We introduce null surfaces (or nullcone fronts) of pseudo-spherical spacelike framed curves in the three-dimensional anti-de Sitter space. These surfaces are formed by the light rays emitted from points on anti-de Sitter spacelike framed curves. We then classify singularities of the nullcone front of a pseudo-spherical spacelike framed curve and show how these singularities are related to the singularities of the associated framed curve. We also define a family of functions called the Anti-de Sitter distance-squared functions to explain the nullcone front of a pseudo-spherical spacelike framed curve as a wavefront from the viewpoint of the Legendrian singularity theory. We finally provide some examples to illustrate the results of this paper.

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O. Ogulcan Tuncer. 2023-05-07. Null surfaces of pseudo-spherical spacelike framed curves in the anti-de Sitter 3-space. https://arxiv.org/abs/2305.04230

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