Geodesic
On the finiteness of the fundamental group of a compact shrinking Ricci soliton
Zhenlei Zhang1
1 Chern Institute of Mathematics Nankai University Tianjin 300071, P.R. China
Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 297-299

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm107-2-9
Keywords: myerss classical theorem says compact riemannian manifold positive ricci curvature has finite fundamental group using ambroses compactness criterion lotts results fern ndez l pez garc a r showed finiteness fundamental group remains valid compact shrinking ricci soliton self contained proof estimating lengths shortest geodesic loops each homotopy class

Zhenlei Zhang 1

1 Chern Institute of Mathematics Nankai University Tianjin 300071, P.R. China 
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Zhenlei Zhang. On the finiteness of the fundamental group
 of a compact shrinking Ricci soliton. Colloquium Mathematicum, Tome 107 (2007) no. 2, pp. 297-299. doi: 10.4064/cm107-2-9

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