具非负Ricci曲率和严格(1+δ)阶体积增长的三维流形  

ON COMPLETE THREE-DIMENSIONAL MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE

作　　者：詹华税[1] 许文彬[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《数学杂志》2009年第1期103-108,共6页Journal of Mathematics

基　　金：福建省自然科学基金(T0650010);集美大学预研基金资助课题

摘　　要：本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质.通过对流形本身与流形的万有覆盖空间体积增长阶的比较,证明了对具非负Ricci曲率和严格(1+δ)阶体积增长的三维完备非紧的黎曼流形是可缩的.The paper studies the geometric and topological properties of a complete noneompact Riemannian three-dimensional manifold with nonegative Ricct curvature. By comparing the volume growth order of the manifold itself to that of its universal covering space, the paper proves that every three-dimensional with nonnegative Ricci curvature and （1＋δ）-order volume growth in strict sense must be contractible provided that its universal covering is finite.

关 键 词：三维流形 非负RICCI曲率 (1+δ)阶体积增长 微分同胚 

分 类 号：O186.12[理学—数学]