高维球冠上的Yamabe问题  

Yamabe Problem on High Dimensional Spherical Cap

作　　者：赖晋秋 胡玉琪 姚纯青[1] LAI Jinqiu;HU Yuqi;YAO Chunqing(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第4期58-62,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971415).

摘　　要：Yamabe问题是微分几何中很重要的一类问题.本文研究了高维球冠M^(n)(n≥4)上的Yamabe问题.首先利用球极投影,将球面上的度量诱导到球冠边界上,计算得到球冠边界的数量曲率;然后提出了球冠上的一类带边界条件的Yamabe方程,并且得到了该方程的一组解.Yamabe problem is an important kind of problem in differential geometry.In this paper,Yamabe problem has been studied on high dimensional spherical cap M^(n)(n≥4).Firstly,the measurement on the sphere is induced to the spherical cap boundary by using spherical pole projection,and the scalar curvature of the spherical cap boundary is calculated.Then,a class of Yamabe Equations with boundary conditions on the spherical cap is proposed,and a set of solutions of the equations are obtained.

关 键 词：Yamabe方程 球冠边界 数量曲率 

分 类 号：O186.1[理学—数学]