The spectral geometry of the Riemann curvature tensor
Differential Geometry
2007-05-23 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.math/0206129,
title = {The spectral geometry of the Riemann curvature tensor},
author = {P. Gilkey and R. Ivanova and T. Zhang},
journal= {arXiv preprint arXiv:math/0206129},
year = {2007}
}