LAUSR

In this paper, we study pseudo-Riemannian submanifolds of a pseudo-hyperbolic space $$\mathbb H^{m-1}_s (-1) \subset \mathbb E^m_{s+1}$$Hsm-1(-1)⊂Es+1m with 2-type pseudo-hyperbolic Gauss map. We give a characterization of proper pseudo-Riemannian hypersurfaces in $$\mathbb H^{n+1}_s (-1) \subset \mathbb E^{n+2}_{s+1}$$Hsn+1(-1)⊂Es+1n+2 with non-zero constant mean curvature and 2-type pseudo-hyperbolic Gauss map. For $$n=2$$n=2, we prove classification theorems. In addition, we show that the hyperbolic Veronese surface is the only maximal surface fully lying in $$\mathbb H^4_2 (-1) \subset \mathbb H^{m-1}_2 (-1)$$H24(-1)⊂H2m-1(-1) with 2-type pseudo-hyperbolic Gauss map. Moreover, we prove that a flat totally umbilical pseudo-Riemannian hypersurface $$M^n_t$$Mtn of the pseudo-hyperbolic space $$\mathbb {H}^{n+1}_t(-1) \subset \mathbb E^{n+2}_{t+1}$$Htn+1(-1)⊂Et+1n+2 has biharmonic pseudo-hyperbolic Gauss map.