Sharp sectional curvature bounds and a new proof of The Spectral Theorem
Differential Geometry
2020-07-15 v1
Abstract
We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to geometrically realize these results to produce a hypersurface with prescribed sectional curvatures at a point. By extending our methods, we give a relatively short proof of the Spectral Theorem for self-adjoint operators on a finite dimensional real vector space.
Keywords
Cite
@article{arxiv.1809.04200,
title = {Sharp sectional curvature bounds and a new proof of The Spectral Theorem},
author = {Maxine Calle and Corey Dunn},
journal= {arXiv preprint arXiv:1809.04200},
year = {2020}
}