A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces
Differential Geometry
2023-05-16 v2
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.
Keywords
Cite
@article{arxiv.2305.03861,
title = {A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces},
author = {Jeffrey S. Case and Aaron J. Tyrrell},
journal= {arXiv preprint arXiv:2305.03861},
year = {2023}
}
Comments
This paper generalizes and supersedes arXiv:2304.08346