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

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.

10 pages