Compact spacelike biconservative hypersurfaces in de Sitter space

TL;DR

This paper studies the geometric properties of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space, revealing new rigidity results in pseudo-Riemannian geometry.

Contribution

It extends the understanding of rigidity properties of spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space.

Findings

Rigidity results for hypersurfaces under geometric constraints

Extension of known properties to pseudo-Riemannian settings

Characterization of hypersurfaces with constant scalar curvature

Abstract

In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space $\mathbb{S}_1^{m+1}(c)$, under some geometric constraints. Our results extend the understanding of rigidity properties of such hypersurfaces in pseudo-Riemannian settings.