Warped product hypersurfaces in the pseudo-Euclidean space

Abstract

We study hypersurfaces in the pseudo-Euclidean space ${\mathbb{E}}_s^{n+1}$, which write as a warped product of a $1$-dimensional base with an $(n-1)$-manifold of constant sectional curvature. We show that either they have constant sectional curvature or they are contained in a rotational hypersurface. Therefore, we first define rotational hypersurfaces in the pseudo-Euclidean space.