Topological structure of complete Riemannian manifolds with cyclic holonomy groups

Michal Sadowski

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Topological structure of complete Riemannian manifolds with cyclic holonomy groups

机译：具有循环完整性组的完整黎曼流形的拓扑结构

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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 or M is diffeomorphic to L*Rm-dimX-1.

机译：令M为具有完整周期整体性的m维维黎曼流形，令X为等效于M的封闭平面多态同质性，令L→X为X上的非平凡线束，其总空间为具有周期整体性的平面流形。我们证明，M对L * Rm-dimX-1是变态的，或者M对L * Rm-dimX-1是变态的。

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《Differential geometry and its applications》 |2005年第2期|共8页
作者
Michal Sadowski;
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正文语种 eng
中图分类微分几何;
关键词
Complete flat manifold; Holonomy group; Topological classification;

机译：完整的平面流形;整体组;拓扑分类;

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专利

1. Topological structure of complete Riemannian manifolds with cyclic holonomy groups [J] . Michal Sadowski Differential geometry and its applications . 2005,第2期

机译：具有循环完整性组的完整黎曼流形的拓扑结构
2. Corrigendum to: Spin structures on flat manifolds with cyclic holonomy [J] . Hiss G., Szczepánski A. Communications in algebra . 2011,第7期

机译：更正为：具有周期性完整性的扁平流形上的自旋结构
3. Spin structures on flat manifolds with cyclic holonomy [J] . Hiss G, Szczepanski A Communications in algebra . 2008,第1期

机译：具有周期完整性的平面流形上的自旋结构
4. Holonomy Groups of Pseudo-Riemannian Manifolds [C] . Aziz Ikemakhen, NATO NATO Advanced Study Institute on Differential Geometry and Topology, Discrete and Computational Geometry . 2005

机译：伪riemannian歧管的全身团体
5. Analysis of conjugate heat equation on complete non-compact Riemannian manifolds under Ricci flow. [D] . Kuang, Shilong. 2009

机译：Ricci流下完全非紧黎曼流形上共轭热方程的分析。
6. ON THE STRUCTURE OF COMPACT RIEMANNIAN MANIFOLDS [O] . W. Klingenberg 1958

机译：关于紧黎曼流形的结构
7. Topological structure of complete Riemannian manifolds with cyclic holonomy groups [O] . Sadowski Michał 2005

机译：具有循环完整性组的完整黎曼流形的拓扑结构

Topological structure of complete Riemannian manifolds with cyclic holonomy groups

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