Lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space

TL;DR

This paper studies lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space, analyzing their singularities using Legendrian singularity theory, contributing to the understanding of geometric structures in Lorentzian manifolds.

Contribution

It introduces a framework for analyzing lightlike hypersurfaces in anti-de Sitter space with general codimension, focusing on their singularities via Legendrian singularity theory.

Findings

Characterization of singularities of lightlike hypersurfaces

Application of Legendrian singularity theory to Lorentzian geometry

Insights into geometric structures in anti-de Sitter space

Abstract

Anti-de Sitter space is the Lorentzian space form with negative curvature. In this paper we consider lightlike hypersurfaces along spacelike submanifolds in anti-de Sitter space with general codimension. In particular, we investigate the singularities of lightlike hypersurfaces as an application of the theory of Legendrian singularities.