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

Jeffrey S. Case; Aaron J. Tyrrell

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arXiv · 2305.03861

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

Jeffrey S. Case·Aaron J. Tyrrell

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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.

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BibTeX RIS

Jeffrey S. Case, Aaron J. Tyrrell. 2023-05-05. A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces. https://arxiv.org/abs/2305.03861

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