Singularities for normal hypersurfaces of de Sitter timelike curves in Minkowski 4-space

Abstract

In this paper, we consider the normal hypersurfaces associated with timelike curves in Minkowski 4-space which are confined in de Sitter 3-space. We classify the generic singularities of the normal hypersurfaces, which are cuspidal edges, swallowtails and butterflies. And reveal the relationships between these singularities and the Lorentzian invariants of timelike curves by applying the singularity theory.