Null surfaces of pseudo-spherical spacelike framed curves in the anti-de Sitter 3-space
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.
Keywords
Cite
@article{arxiv.2305.04230,
title = {Null surfaces of pseudo-spherical spacelike framed curves in the anti-de Sitter 3-space},
author = {O. Ogulcan Tuncer},
journal= {arXiv preprint arXiv:2305.04230},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2304.08045