  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.
