标量曲率衰竭的黎曼流形上的空隙定理  

Gap Theorem on Riemannian Manifold with Decaying Scalar Curvature

作　　者：阮其华[1] 陈志华[1] 

机构地区：[1]同济大学应用数学系

出　　处：《同济大学学报（自然科学版）》2005年第10期1401-1406,共6页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(10271089);福建省教育厅资助项目(JA04266)

摘　　要：通过Yamabe流的研究,证明了对任一完备非紧局部共形平埋的黎曼流形,若Ricci曲率非负,标量曲率有界且它的平均值满足一定衰竭条件,则此流形是平坦的.In this paper, through studying Yamabe flow, we prove that for any complete noncompact locally conformally flat manifolds, if the Ricci curvature is nonnegative, the scalar curvature is bounded and the mean value of the scalar curvature satisfies some decaying condition, then the manifold is flat.

关 键 词：空隙定理 标量曲率 Yamabe流 

分 类 号：O186.16[理学—数学]