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

• Autorzy: Zhenlei Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
• 55Q52: Homotopy groups of special spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 2
• Strony: 297-299

Daty

wydano

2007

Twórcy

autor

Zhenlei Zhang

• Chern Institute of Mathematics, Nankai University, Tianjin 300071, P.R. China

Identyfikatory

DOI

10.4064/cm107-2-9