On spacelike surfaces in Anti de Sitter 3-space from the contact viewpoint

Abstract

We study differential geometry of spacelike surfaces in Anti de Sitter 3-space from the contact viewpoint. We define the timelike Anti de Sitter Gauss images and timelike Anti de Sitter height functions on spacelike surfaces and investigate the geometric meanings of singularities of these mappings. We consider the contact of spacelike surfaces with models (so-called AdS-great-hyperboloids) as an application of Legendrian singularity theory.