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具非负Ricci曲率和严格(1+δ)阶体积增长的三维流形 被引量：1

ON COMPLETE THREE-DIMENSIONAL MANIFOLDS WITH NONNEGATIVE RICCI CURVATURE
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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.
作者 詹华税 许文彬
机构地区 集美大学理学院
出处 《数学杂志》 CSCD 北大核心 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
关键词 三维流形 非负RICCI曲率 (1+δ)阶体积增长 微分同胚 Three-dimensional manifold nonnegative Ricci curvature （1＋δ）-order volume growth diffeomorphism
分类号 O186.12 [理学—基础数学]
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参考文献16

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二级参考文献12

  • 1伍鸿熙，黎曼几何选讲，1993年
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数学杂志
2009年 第1期

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