Year: 2020
Author: Yun Miao, Liqun Qi, Yimin Wei
Communications in Mathematical Research , Vol. 36 (2020), Iss. 3 : pp. 336–353
Abstract
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold. The expressions of M-eigenvalues and M-eigenvectors are presented in this 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 reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold. We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely. We also give an example to compute the M-eigentriple of de Sitter spacetime which is well-known in general relativity.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0052
Communications in Mathematical Research , Vol. 36 (2020), Iss. 3 : pp. 336–353
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: M-eigenvalue Riemann curvature tensor Ricci tensor conformal invariant canonical form.