A rigidity theorem for hypersurfaces of the odd-dimensional unit sphere $\mathbb S^{2n+1}(1)$

Abstract

We establish an optimal integral inequality for closed hypersurfaces in the odd-dimensional unit sphere $\mathbb S^{2n+1}(1)$ with vanishing Reeb function that involves the shape operator $A$ and the contact vector field $U$. The integral inequality is op