Ricci pinched compact hypersurfaces in spheres

TL;DR

This paper studies the topology of compact hypersurfaces in spheres with Ricci curvature bounds related to their mean curvature, using Bochner techniques to derive stronger results than previous methods.

Contribution

It introduces new topological results for hypersurfaces in spheres with Ricci curvature bounds, improving upon earlier findings by employing Bochner techniques.

Findings

Stronger topological restrictions for hypersurfaces with Ricci bounds

Application of Bochner technique yields improved results

Enhanced understanding of hypersurface geometry in spheres

Abstract

We investigate the topology of the compact hypersurfaces in round spheres whose Ricci curvature satisfies an appropriate bound that only depends on the mean curvature of the submanifold. In this paper, the use of the Bochner technique allows same stronger results than the ones obtained by us in the case of submanifolds lying in any codimension.