A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces

Abstract

We derive a sharp inequality relating the second and fourth elementary symmetric functions of the eigenvalues of a trace-free matrix and give two applications. First, we give a new proof of the classification of conformally flat hypersurfaces in spaceforms. Second, we construct a functional which characterizes rotational hypersurfaces and catenoids.

This paper generalizes and supersedes arXiv:2304.08346