The structure of complete manifolds of nonnegative curvature
The structure of complete manifolds of nonnegative curvature
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DOI：
10.1090/s0002-9904-1968-12088-9
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发表时间：
1968-11
影响因子：
1.3
通讯作者：
J. Cheeger;Detlef Gromoll
中科院分区：
文献类型：
--
作者：
J. Cheeger;Detlef Gromoll
0.本文给出了非负截面曲率完备流形结构的一些结果。(We将用M表示这样的流形。）详细信息和相关结果将在其他地方出现。我们的工作推广了Gromoll、Meyer [2]和Toponogov [4]的工作。我们的分析分为两个部分。第一，我们觉得是特别感兴趣的，基本上减少了研究的拓扑结构的完整的流形的非负曲率的紧致流形的非负曲率。第二步将紧致流形的情形简化为紧致单连通流形（模紧致平坦流形的分类）。我们的结果有各种应用。其中之一是分类的等距完整的三维流形的非负曲率。
0. In this paper we describe some results on the structure of complete manifolds of nonnegative sectional curvature. (We will denote such manifolds by M.) Details and related results will appear elsewhere. Our work generalizes that of Gromoll, Meyer [2] as well as Toponogov [4]. Our analysis is divided into two parts. The first, which we feel is of particular interest, essentially reduces the study of the topology of complete manifolds of nonnegative curvature to that of compact manifolds of nonnegative curvature. The second step reduces the compact case to the compact simply connected case (modulo the classification of compact flat manifolds). Our results have various applications. One of these is the classification up to isometry of complete 3-dimensional manifolds of nonnegative curvature.