Singularities of tangent lightcone map of a timelike surface in Minkowski 4-space

Abstract

In the paper, we will define tangent lightcone map, tangentlightcone curvature and tangent lightcone height function. Then we study the geometry of the timelike surfaces in Minkowski 4-space through their contact with spacelike hyperplane and give the classification of singularities of tangent lightcone map based on the Legendrian singularity theory of Arnol'd.