极小模原理的一类四阶张量的不等式应用

Application of the Minimal NormalTensors to a Class of Fourth-Order TensorInequalities

摘要: 本文研究了n维Ricci-半对称黎曼流形Mⁿ上的Ricci 曲率张量Ric 的二阶协变导数R_ij,kl极小模张量，并且得到了关于Ricci曲率张量的二阶协变导数的一个不等式$${\Vert {\mathrm{\nabla }}^{2}Ric\Vert }^2\ge \frac{n^2+2n-4}{n(n-2)(n+4)}{\Vert \mathrm{\Delta }Ric\Vert }^2$$。

Abstract: In this paper, we investigate the minimal norm tensors of the second-order covariant derivative R_ij,kl of the Ricci curvature tensor Ric on an n-dimensional Ricci-semisymmetric Riemannian manifold Mⁿ, and derive an inequality for the second order covariant derivative of the Ricci curvature tensor $${\Vert {\mathrm{\nabla }}^{2}Ric\Vert }^2\ge \frac{n^2+2n-4}{n(n-2)(n+4)}{\Vert \mathrm{\Delta }Ric\Vert }^2$$.