Minimal hypersurfaces in $\mathbb{S}^5$ with constant scalar curvature and zero Gauss curvature are totally geodesic

TL;DR

This paper proves that certain minimal hypersurfaces in a 5-sphere with specific curvature conditions are necessarily totally geodesic, contributing to the classification of such geometric structures.

Contribution

It establishes a rigidity result for minimal hypersurfaces in $ ext{S}^5$ with constant scalar curvature and zero Gauss curvature, showing they must be totally geodesic.

Findings

Minimal hypersurfaces with given curvature conditions are totally geodesic.

Provides a classification result for hypersurfaces in $ ext{S}^5$.

Enhances understanding of curvature constraints in differential geometry.

Abstract

We show that a closed minimal hypersurface in $\mathbb{S}^5$ with constant scalar curvature and zero Gauss curvature is totally geodesic.