中国科技纵横
中國科技縱橫
중국과기종횡
CHINA SCIENCE & TECHNOLOGY PANORAMA MAGAZINE
2011年
17期
151-151,162
,共2页
黎曼曲率%Ricci曲率%数量曲率
黎曼麯率%Ricci麯率%數量麯率
려만곡솔%Ricci곡솔%수량곡솔
Riemannian curvature%Ricci curvature%scalar curvature
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．
本文研究緊緻連通定嚮光滑n（n≥3）維流形M^n上一類由黎曼麯率張量、Ricci麯率張量的L^2模和數量麯率的平方的細閤歿關于度量g的體積元的閤適冪法化後定義的黎曼汎函F的臨界度量，採用活動標架法得到汎函F的Euler-Lagrange方程，以及任意Einstein度量是汎函F的臨界度量的一些充分條件．
본문연구긴치련통정향광활n（n≥3）유류형M^n상일류유려만곡솔장량、Ricci곡솔장량적L^2모화수량곡솔적평방적세합몰관우도량g적체적원적합괄멱법화후정의적려만범함F적림계도량，채용활동표가법득도범함F적Euler-Lagrange방정，이급임의Einstein도량시범함F적림계도량적일사충분조건．
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.
