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.

引用

页码：106 / 113

页数：8

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