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The spectral geometry of the Riemann curvature tensor

P. Gilkey·R. Ivanova·T. Zhang
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Abstract

Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. This survey article studies when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. It deals with results for the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the skew-symmetric curvature operator. Some results in the complex setting are presented as well for the skew-symmetric curvature operator.

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P. Gilkey, R. Ivanova, T. Zhang. 2002-06-12. The spectral geometry of the Riemann curvature tensor. https://arxiv.org/abs/math/0206129

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