2018/07/28 by Yun Miao, Liqun Qi, Miao, Yun +3
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1808.01882
openalex publication_date 2018/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.