关于黎曼泛函临界度量的—些结果

本文研究紧致连通定向光滑n（n≥3）维流形M^n上一类由黎曼曲率张量、Ricci曲率张量的L^2模和数量曲率的平方的细合殁关于度量g的体积元的合适幂法化后定义的黎曼泛函F的临界度量，采用活动标架法得到泛函F的Euler-Lagrange方程，以及任意Einstein度量是泛函F的临界度量的一些充分条件．

Critical metrics of a Riemannian functional

In this paper, we study critical metrics of a Riemannian functionalF on a compact, connected smooth orientable n -manifold M^n, n ≥ 3 , defined by the combination of L2-norm of Riemannian curvature tensor. Ricci tensor and the square of scalar curvature, normalized by an appropriate power of the volume of M6n with respect to Riemannian metric g, We compute the Euler-Lagrange equations of functionalF by using the moving frame, and find some sufficient conditions for any Einstein metric to be critical metrics of functionalF.