Warped product hypersurfaces in the pseudo-Euclidean space

TL;DR

This paper classifies warped product hypersurfaces in pseudo-Euclidean space, showing they either have constant sectional curvature or are part of a rotational hypersurface, and introduces the concept of rotational hypersurfaces in this setting.

Contribution

It provides a classification of warped product hypersurfaces in pseudo-Euclidean space and defines rotational hypersurfaces within this context.

Findings

Hypersurfaces are either of constant sectional curvature or contained in a rotational hypersurface.

Introduces the concept of rotational hypersurfaces in pseudo-Euclidean space.

Provides a classification result for warped product hypersurfaces.

Abstract

We study hypersurfaces in the pseudo-Euclidean space $\mathbb{E}^{n+1}_s$, 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.