On submanifolds of pseudo-hyperbolic space with 1-type pseudo-hyperbolic Gauss map

In this paper, we examine pseudo-Riemannian submanifolds of a pseudo-hyperbolic space $\mathbb H^{m-1}_s (-1) \subset \mathbb E^m_{s+1}$ with finite type pseudo-hyperbolic Gauss map. We begin by providing a characterization of pseudo-Riemannian submanifolds in $\mathbb H^{m-1}_s (-1)$ with 1-type pseudo-hyperbolic Gauss map, and we obtain the classification of maximal surfaces in $\mathbb H^{m-1}_2 (-1) \subset \mathbb E^m_{3}$ with 1-type pseudo-hyperbolic Gauss map. Then we investigate the submanifolds of $\mathbb H^{m-1}_s (-1)$ with 1-type pseudo-hyperbolic Gauss map containing nonzero constant component in its spectral decomposition.