A Rigidity Theorem for Spacelike Hypersurfaces in de Sitter Space

TL;DR

This paper proves a rigidity theorem for spacelike hypersurfaces with curvature restrictions in de Sitter space, extending known results from Riemannian space forms to Lorentzian geometry.

Contribution

It introduces a new rigidity theorem for spacelike hypersurfaces in de Sitter space with specific curvature conditions, analogous to previous Riemannian results.

Findings

Establishes a rigidity condition for spacelike hypersurfaces in de Sitter space.

Extends classical rigidity results from Riemannian to Lorentzian geometry.

Provides a new characterization of hypersurfaces under curvature restrictions.

Abstract

In this paper we present a rigidity theorem for locally isometric hypersurfaces with a curvature restriction in de Sitter space. This is an analogue to the case for Riemannian space forms given by Guan and Shen in [5].