$S_t^1\times S_s^1$-valued lightcone Gauss map of a Lorentzian surface in semi-Euclidean 4-space

TL;DR

This paper introduces $S_t^1 imes S_s^1$-valued lightcone Gauss maps and related geometric concepts for Lorentzian surfaces in semi-Euclidean 4-space, linking singularities to surface invariants using singularity theory techniques.

Contribution

It defines new lightcone geometric invariants and establishes their relationship with singularities, advancing the understanding of Lorentzian surface geometry in semi-Euclidean space.

Findings

Relationships between singularities and geometric invariants established

Definitions of lightcone Gauss maps and pedal surfaces provided

Applications of singularity theory techniques to Lorentzian lightcone height functions

Abstract

We define the notions of $S_t^1\times S_s^1$-valued lightcone Gauss maps, lightcone pedal surface and Lorentzian lightcone height function of Lorentzian surface in semi-Euclidean 4-space and established the relationships between singularities of these objects and geometric invariants of the surface as applications of standard techniques of singularity theory for the Lorentzian lightcone height function.