Singularities of Anti de Sitter torus Gauss maps
The authors study the time-like surfaces in anti de Sitter (adS) 3-spacetime, by analogy with similar researches for Minkowski and de Sitter cases. The main idea is to use techniques from singularity theory and find properties of submanifold geometry from the analysis of the singularities of specific contact functions. The basic ingredients the authors define and rely on are: the adS-nullcone Gauss image, the adS-torus Gauss map, the adS-null Gauss-Kronecker curvature, the adS-torus Gauss-Kronecker curvature, the adS-null height function, the adS-torus cylindrical pedal and the adS-null Monge form. Using these notions, several results are proven, including a generic classification of the singularities of adS-nullcone Gauss image and of the adS-torus Gauss map.
scientific article; zbMATH DE number 5703332
scientific article