Ricci Curvature, Diameter and Fundamental groups

2005/02/14 by Wen-Haw Chen, Jyh-Yang Wu, Chen, Wen-Haw +1
Mathematics · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0502281

17 pages

arxiv created 2005/02/14 · openalex publication_date 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we discuss the fundamental groups and diameters of positively Ricci curved n-manifolds. We use a method combining the results about equivarient Hausdorff convergence developed by Fukaya and Yamaguchi with the Ricci version of splitting theorem by Cheeger and Colding to give new information on the topology of compact manifolds with positive Ricci curvature. Moreover, we also obtain a weak Margulis's lemma for manifolds under a lower Ricci curvature bound.

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