Constant-Mean-Curvature Surfaces with Singularities in Minkowski 3-Space

Abstract

We shall investigate spacelike constant-mean-curvature surfaces with singularities in Minkowski 3-space. Recently, Kokubu, Rossman, Saji, Umehara, and Yamada gave useful criteria for cuspidal edges and swallowtails. Applying their criteria, we define a new class of generalized constant-mean-curvature surface and give some examples with cuspidal edges and swallowtails.

Keywords:

• Primary 53A10
• Secondary 53C43, 53C50
• CMC surface
• Gauss map
• cuspidal edge
• swallowtail
• singularity