Topological structure of complete Riemannian manifolds with cyclic holonomy groups

被引：1
|
作者：
Sadowski, M [1 ]
机构：
[1] Univ Gdansk, Dept Math, PL-80952 Gdansk, Poland
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2005年 / 23卷 / 02期
关键词：
complete flat manifold; holonomy group; topological classification;
D O I：
10.1016/j.difgeo.2005.05.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let M be a complete m-dimensional Riemannian manifold with cyclic holonomy group, let X be a closed flat manifold homotopy equivalent to M, and let L -> X be a nontrivial line bundle over X whose total space is a flat manifold with cyclic holonomy group. We prove that either M is diffeomorphic to X x Rm-dim X or M is diffeomorphic to L x Rm-dim X-1. (c) 2005 Elsevier B.V. All rights reserved.
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页码：106 / 113
页数：8
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