A+ CATEGORY SCIENTIFIC UNIT

On the finiteness of the fundamental group of a compact shrinking Ricci soliton

Volume 107 / 2007

Zhenlei Zhang Colloquium Mathematicum 107 (2007), 297-299 MSC: Primary 53C25; Secondary 53C21, 55Q52. DOI: 10.4064/cm107-2-9

Abstract

Myers's classical theorem says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Using Ambrose's compactness criterion or J. Lott's results, M. Fernández-López and E. García-Río showed that the finiteness of the fundamental group remains valid for a compact shrinking Ricci soliton. We give a self-contained proof of this fact by estimating the lengths of shortest geodesic loops in each homotopy class.

Authors

  • Zhenlei ZhangChern Institute of Mathematics
    Nankai University
    Tianjin 300071, P.R. China
    e-mail

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