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Volume 36, Issue 3
M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds

Yun Miao, Liqun Qi & Yimin Wei

DOI: 10.4208/cmr.2020-0052

Commun. Math. Res., 36 (2020), pp. 336-353.

Published online: 2020-07

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  • 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.

  • Keywords

M-eigenvalue, Riemann curvature tensor, Ricci tensor, conformal invariant, canonical form.

  • AMS Subject Headings

15A48, 15A69, 65F10, 65H10, 65N22

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-36-336, author = {Miao , YunQi , Liqun and Wei , Yimin}, title = {M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {3}, pages = {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.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0052}, url = {http://global-sci.org/intro/article_detail/cmr/17852.html} }
TY - JOUR T1 - M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds AU - Miao , Yun AU - Qi , Liqun AU - Wei , Yimin JO - Communications in Mathematical Research VL - 3 SP - 336 EP - 353 PY - 2020 DA - 2020/07 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0052 UR - https://global-sci.org/intro/article_detail/cmr/17852.html KW - M-eigenvalue, Riemann curvature tensor, Ricci tensor, conformal invariant, canonical form. AB -

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.

Miao , YunQi , Liqun and Wei , Yimin. (2020). M-Eigenvalues of the Riemann Curvature Tensor of Conformally Flat Manifolds. Communications in Mathematical Research . 36 (3). 336-353. doi:10.4208/cmr.2020-0052
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