Singularities of Slant Focal Surfaces along Lightlike Locus on Mixed Type Surfaces

Abstract

There are generally the mixed type surfaces with lightlike locus in the Lorentz-Minkowski 3-space. To investigate the geometry of lightlike locus, we define slant focal surfaces and slant evolutes associated to the oringinal mixed type surface by using a moving frame field along the lightlike locus defined by Honda etc. We obtain that singularities of slant focal surfaces and slant evolutes depend on the differential geometric properties of the lightlike locus. Furthermore, we investigate the relationship between slant focal surfaces and slant evolutes. We also consider the relationship between slant evolutes and the lightlike locus on the lightcone.