Singularity Analysis of Lightlike Hypersurfaces Generated by Null Cartan Curves in Minkowski Spacetime - Xiaoming Fan; Yongsheng Zhu; Haijing Pan (Axioms)
This study investigates the singularity structures of lightlike hypersurfaces generated by null Cartan curves in Minkowski spacetime. We construct a hierarchical geometric framework consisting of a lightlike hypersurface <semantics>LHβ</semantics>, a critical lightlike surface <semantics>LSβ</semantics>, and a degenerate curve <semantics>LCβ</semantics>, with dimensions decreasing from 3D to 1D. Using singularity theory, we identify a novel geometric invariant <semantics>σ(t)</semantics> that governs the emergence of specific singularity types, including <semantics>C(2,3)×R2</semantics>, <semantics>SW×R</semantics>, <semantics>BF</semantics>, <semantics>C(BF)</semantics>, <semantics>C(2,3,4)×R</semantics>, and <semantics>(2,3,4,5)</semantics>-cusp. These singularities exhibit increasing degeneracy as the hierarchy progresses, with contact orders between the lightlike hyperplane <semantics>H<msubsup>St0L</msubsup></semantics> and the curve <semantics>β</semantics> systematically intensifying. An explicit example demonstrates the construction of these objects and validates the theoretical results. This work establishes a systematic connection between null Cartan curves, stratified singularities, and contact geometry.