Compact Biconservative Hypersurfaces in Space Forms: Rigidity Without Scalar Curvature Assumptions

TL;DR

This paper proves rigidity results for compact biconservative hypersurfaces in space forms without assuming constant scalar or sectional curvature, using a new divergence-free tensor.

Contribution

Introduces a novel divergence-free tensor to establish rigidity of hypersurfaces without curvature assumptions.

Findings

Rigidity results for hypersurfaces without scalar curvature constraints

New divergence-free tensor as a key analytical tool

Results applicable to general space forms

Abstract

In this study, we investigate the intrinsic properties of compact biconservative hypersurfaces in space forms. In this framework, we establish rigidity results without imposing the assumption of constant scalar curvature. Furthermore, we present an additional result that does not require any assumptions on the sectional curvature. The key tool in our approach is the introduction of a novel divergence-free tensor, which enables us to derive these results without the usual curvature assumptions.