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

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 .

Abstract: 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).