English

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

Differential Geometry 2023-05-09 v1

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