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Complete shrinking Ricci solitons have finite fundamental group
Author(s):
William
Wylie
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1803-1806.
MSC (2000):
Primary 53C20
Posted:
October 18, 2007
MathSciNet review:
2373611
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Abstract:
We show that if a complete Riemannian manifold supports a vector field such that the Ricci tensor plus the Lie derivative of the metric with respect to the vector field has a positive lower bound, then the fundamental group is finite. In particular, it follows that complete shrinking Ricci solitons and complete smooth metric measure spaces with a positive lower bound on the Bakry-Emery tensor have finite fundamental group. The method of proof is to generalize arguments of García-Río and Fernández-López in the compact case.
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Additional Information:
William
Wylie
Affiliation:
Department of Mathematics, University of California, Los Angeles, California 90095
Email:
wylie@math.ucla.edu
DOI:
10.1090/S0002-9939-07-09174-5
PII:
S 0002-9939(07)09174-5
Keywords:
Ricci soliton,
noncompact manifold,
fundamental group
Received by editor(s):
March 29, 2007
Posted:
October 18, 2007
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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