A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces
Jeffrey S. Case, Aaron J. Tyrrell · arXiv (Cornell University) · 2023
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.