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

Zhenlei Zhang. "On the finiteness of the fundamental group of a compact shrinking Ricci soliton." Colloquium Mathematicae 107.2 (2007): 297-299. <http://eudml.org/doc/283451>.

@article{ZhenleiZhang2007,
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.},
author = {Zhenlei Zhang},
journal = {Colloquium Mathematicae},
keywords = {Ricci soliton; fundamental group},
language = {eng},
number = {2},
pages = {297-299},
title = {On the finiteness of the fundamental group of a compact shrinking Ricci soliton},
url = {http://eudml.org/doc/283451},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Zhenlei Zhang
TI - On the finiteness of the fundamental group of a compact shrinking Ricci soliton
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 2
SP - 297
EP - 299
AB - 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.
LA - eng
KW - Ricci soliton; fundamental group
UR - http://eudml.org/doc/283451
ER -