论文摘要
本文内容分两章.第一章中,我们研究给定紧致连通定向光滑n（n≥3）维流形Mn上的Riemann泛函（?）的临界度量,该泛函由无迹的Ricci张量的L2模及关于Riemann度量g的Mn的体积元的合适幂法化后定义,即:其中Eg=Ricg-（?）g表示无迹的Ricci张量,Ricg和Rg表示关于Riemann度量g的Ricci张量和数量曲率.可以证明,该泛函的临界度量有重要的性质,它的局部共形平坦临界度量的性质也可获得.第二章中，我们研究一类特殊的Riemann泛函F,它定义为:其中a,b,c关于Riemann流形的维数n是不全为零的任意常数,Riemg表示关于Riemann度量g的Riemann曲率张量.我们计算泛函F的Euler-Lagrange方程,可以发现在某些条件下,泛函F的局部共形平坦临界度量也是Einstein度量.
论文目录
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标签：泛函论文; 临界度量论文; 局部共形平坦度量论文; 空间形式论文;