Pseudo‐hyperbolic Gauss maps of Lorentzian surfaces in anti‐de Sitter space

In this paper, we determine the type numbers of the pseudo‐hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non‐diagonalizable shape operator in the 3‐dimensional anti‐de Sitter space. Also, we investigate the behavior of type numbers of the pseudo‐hyperbolic Gauss map along the parallel family of such oriented Lorentzian surfaces in the 3‐dimensional anti‐de Sitter space. Furthermore, we investigate the type number of the pseudo‐hyperbolic Gauss map of one of Lorentzian hypersurfaces of B‐scroll type in a general dimensional anti‐de Sitter space.