The spectral geometry of the Riemann curvature tensor

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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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Differential Geometry, Mathematical Physics, 53B20

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http://salesiana.dossiersoluciones.com/handle/123456789/64292

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206129
 http://arxiv.org/abs/math/0206129

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arXiv