SINGULARITIES OF TANGENT LIGHTCONE MAP OF A TIMELIKE SURFACE IN MINKOWSKI 4-SPACE

Abstract

In the paper, we will define tangent lightcone map, tangent lightcone 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.