Null Surfaces of Pseudo-spherical Spacelike Framed Curves in the Anti-de Sitter 3-space

作     者：Tuncer, O. Oǧulcan 

作者机构：Department of Mathematics Hacettepe University Ankara Turkey 

出 版 物：《Acta Mathematica Sinica, English Series》 (数学学报（英文版）)

年 卷 期：2024年第40卷第12期

页      面：3043-3054页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Nullcone front anti-de Sitter space framed curve distance-squared function 

摘      要：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.