Vol. 13, No. 3, 2020

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Sharp sectional curvature bounds and a new proof of the spectral theorem

Maxine Calle and Corey Dunn

Vol. 13 (2020), No. 3, 445–454
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
sectional curvature, canonical algebraic curvature tensor, spectral theorem
Mathematical Subject Classification 2010
Primary: 15A69
Secondary: 15A63, 53C21
Milestones
Received: 16 October 2019
Revised: 17 March 2020
Accepted: 28 April 2020
Published: 14 July 2020

Communicated by Frank Morgan
Authors
Maxine Calle
Reed College
Portland, OR
United States
Corey Dunn
Mathematics Department
California State University at San Bernardino
San Bernardino, CA
United States