常数量曲率黎曼度量之共形形变(英文)  

Conformal deformation of a Riemannian metric to constant scalar curvature

作　　者：赵培标[1] 

机构地区：[1]南京理工大学应用数学系,江苏南京210094

出　　处：《信阳师范学院学报（自然科学版）》2003年第2期146-149,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：Supported by NNSF(1 9771 0 48) and the Mid-Young Main Teacherof Anhui Province(JW990 1 5 5 )

摘　　要：本文考查光滑黎曼流形 ( Mn ,g) ( n≥ 2 )的共形形变 .证明了如下结论 :存在共形于度量 g的黎曼度量 g使得 g的曲率 R等于一个事先给定的函数 K .This paper deals with the conformal deformation of the smooth Riemannian manifold(Mn,g)(n≥2).It is proved,in some case,there exists a Riemannian metric g which is conformal to g such that the scalar curvature R of g is equal to K(K is a given function).

关 键 词：光滑黎曼流形 黎曼度量 共形形变 常数量曲率 椭圆方程 上解 微分几何 

分 类 号：O186.12[理学—数学]