M-eigenvalues of Riemann Curvature Tensor of Conformally Flat Manifolds
Abstract
We generalized Xiang, Qi and Wei's results on the M-eigenvalues of Riemann curvature tensor to higher dimensional conformal flat manifolds. The expression of M-eigenvalues and M-eigenvectors are found in our paper. As a special case, M-eigenvalues of conformal flat Einstein manifold have also been discussed, and the conformal the invariance of M-eigentriple has been found. We also discussed the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold. We proved that the M-eigenvalue can determine the Riemann curvature tensor uniquely and generalize the real M-eigenvalue to complex cases. In the last part of our paper, we give an example to compute the M-eigentriple of de Sitter spacetime which is well-known in general relativity.
Keywords
Cite
@article{arxiv.1808.01882,
title = {M-eigenvalues of Riemann Curvature Tensor of Conformally Flat Manifolds},
author = {Yun Miao and Liqun Qi and Yimin Wei},
journal= {arXiv preprint arXiv:1808.01882},
year = {2018}
}