Rigidity results for compact biconservative hypersurfaces in space forms

TL;DR

This paper provides alternative proofs for existing rigidity results and introduces new rigidity theorems for compact biconservative hypersurfaces in space forms, based on curvature estimates.

Contribution

It offers new rigidity results by replacing curvature assumptions with shape operator estimates, expanding understanding of hypersurface geometry.

Findings

Alternative proofs for known rigidity theorems

New rigidity results under shape operator estimates

Extension of rigidity conditions beyond non-negative curvature

Abstract

In this paper we present alternative proofs for two known rigidity results concerning non-negatively curved compact biconservative hypersurfaces in space forms. Further, we prove some new rigidity results by replacing the hypothesis of non-negative sectional curvature with some estimates of the squared norm of the shape operator.