Lightlike hypersurfaces and lightlike focal sets with respect to Bishop frame in 4-dimensional Minkowski Space E1-4.

Abstract

In this article, light-like hypersurfaces which are derived by null Cartan curves are examined and discussed. The singularities of lightlike hypersurfaces and light-like focal sets are investigated by using the Bishop frame on the Null Cartan curves. We obtain that the types of these singularities and the order of contact between the null Cartan curves are closely related to the Bishop curvatures of the null Cartan curves. Moreover, two examples of light-like hypersurfaces and light-like focal sets are given to illustrate our theoretical results.