Curves in a spacelike hypersurface in Minkowski space-time

Abstract

In mathematical physics, Minkowski space (or Minkowski space-time) is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold.

The hyperbolic surface and de Sitter surface of a curve are defined in the spacelike hypersurface $M$ in Minkowski $4$-space and located, respectively, in hyperbolic 3-space and de Sitter 3-space. In this study, techniques from singularity theory were applied to obtain the generic shape of such surfaces and their singular value sets and the geometrical meanings of these singularities were investigated.