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 - <p style="text-align: justify;">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.</p>