摘要
p阶Gauss-Bonnet-Chern曲率L_p是数量曲率的一种推广.本文考虑了由此曲率定义的黎曼泛函F^p.计算了F^p的二阶变分公式.应用该公式证明了球面上的标准度量和复射影空间上的Fubini-Study度量是F^p的鞍点.
The p-th Gauss-Bonnet-Chern curvature Lp is a generalization of the scalar curvature. We consider the Riemannian functional F^P defined by this curvature. In this paper, we calculate the second variational formula of FP. As its application, we prove that the standard metric of the unit sphere and the Fubini-Study metric of the complex projective space are saddle points for F^P.
作者
郭希
吴岚
GUO Xi1, WU Lan2(1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, Hubei, 430062, P. R. China; 2. Department of Mathematics, School of Information, Renmin University of China, Beijing, 100872, P. R. Chin)
出处
《数学进展》
CSCD
北大核心
2018年第2期231-242,共12页
Advances in Mathematics（China）
基金
supported by NSFC(No.11501184)
