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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
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Abstract |
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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. |
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Keywords
sectional curvature, canonical algebraic curvature tensor,
spectral theorem
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Mathematical Subject Classification 2010
Primary: 15A69
Secondary: 15A63, 53C21
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Milestones
Received: 16 October 2019
Revised: 17 March 2020
Accepted: 28 April 2020
Published: 14 July 2020
Communicated by Frank Morgan
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Authors |
| Maxine Calle | |
| Reed College Portland, OR United States |
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| Corey Dunn | |
| Mathematics Department California State University at San Bernardino San Bernardino, CA United States |
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