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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons


Authors: Manuel Fernández-López and Eduardo García-Río
Journal: Proc. Amer. Math. Soc. 141 (2013), 2145-2148
MSC (2010): Primary 53C25, 53C20, 53C44
Published electronically: February 7, 2013
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Abstract: We give a sharp lower bound for the scalar curvature of a steady gradient Ricci soliton in terms of the hyperbolic secant of the distance from a fixed point under the assumption that $ 2\vert Rc\vert^2\leq R^2$, a condition that is satisfied by any steady gradient Ricci soliton with nonnegative sectional curvature.


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Additional Information

Manuel Fernández-López
Affiliation: Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email: manufl@edu.xunta.es

Eduardo García-Río
Affiliation: Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
Email: eduardo.garcia.rio@usc.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11675-8
PII: S 0002-9939(2013)11675-8
Keywords: Gradient Ricci soliton, scalar curvature.
Received by editor(s): October 6, 2011
Published electronically: February 7, 2013
Communicated by: Lei Ni
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.