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.
Citation
Maxine Calle. Corey Dunn. "Sharp sectional curvature bounds and a new proof of the spectral theorem." Involve 13 (3) 445 - 454, 2020. https://doi.org/10.2140/involve.2020.13.445
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