Pseudo-spherical evolutes of lightlike loci on mixed type surfaces in Minkowski 3-space

A surface with nonempty timelike, lightlike, and spacelike points in Minkowski 3-space is a mixed type surface. The mixed type surface has a signature-changing metric, and its lightlike points can be seen as singularities of such metric. In this paper, we study singular properties of pseudo-spherical evolutes of lightlike loci on mixed type surfaces. We classify the generic singularities of pseudo-spherical evolutes by the singularity theory. These singularities and the contact between lightlike loci and model submanifolds are closely associated. We also show the Legendrian duality among pseudo-spherical evolutes, lightlike loci, and Darboux vectors. Moreover, the singularities of pseudo-spherical evolutes are studied from the viewpoint of opening map-germ. Finally, we give an example to demonstrate the theoretical results.