Work

Singularity Analysis of Lightlike Hypersurfaces Generated by Null Cartan Curves in Minkowski Spacetime

Year: 2025

Type: article

Abstract: 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 LHβ, a critical lightlike surface LSβ, and a degenerate curve LCβ, with dimensions decreasing from 3D to 1D. Using singularity theory, we identify a novel geometric invariant σ(t) that governs the emergence of specific singularity types, including C(2,3)×R2, SW×R, BF, C(BF), C(2,3,4)×R, and (2,3,4,5)-cusp. These singularities exhibit increasing degeneracy as the hierarchy progresses, with contact orders between the lightlike hyperplane HSt0L and the curve β 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.

Source: Axioms

DOI: 10.3390/axioms14040279

Authors: Xiaoming Fan, Yongsheng Zhu, Haijing Pan

Institution: Harbin Normal University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Natural Science Foundation of Heilongjiang Province