Compact affine manifolds with precompact holonomy are geodesically complete

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:436

Article

Ake Hau, Luis Alberto¹  Sanchez, Miguel² 

[1] Univ Malaga, Fac Ciencias, Dept Algebra Geometria & Topol, Campus Univ Teatinos, Malaga 29080, Spain

[2] Univ Granada, Fac Ciencias, Dept Geometria & Topol, Campus Fuentenueva S-N, E-18071 Granada, Spain

关键词: Linear connections;    Geodesic completeness;    Holonomy;    Affine manifolds;    Lorentzian and semi-Riemannian manifolds;    Extendibility solutions ODE;   

DOI  :  10.1016/j.jmaa.2015.12.037

来源: Elsevier

【 摘 要 】

This note proves the geodesic completeness of any compact manifold endowed with a linear connection such that the closure of its holonomy group is compact. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free