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The Quarterly Journal of Mathematics Advance Access published online on February 17, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap006
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

DIAMETER BOUNDS AND HITCHIN-THORPE INEQUALITIES FOR COMPACT RICCI SOLITONS

Manuel Fernández-López {dagger} and Eduardo García-Río{ddagger}

Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain

{ddagger} Corresponding author. E-mail: eduardo.garcia.rio{at}usc.es

Received 18 September 2008; Accepted for publication 16 January 2009.


  Abstract

We give lower bounds for the diameter of a compact Ricci soliton depending on the scalar and Ricci curvatures as well as on the range of the potential function, which do not depend on the dimension of the manifold. As an application, sufficient conditions are provided for a four-dimensional compact Ricci soliton to satisfy the Hitchin-Thorpe inequality.

{dagger} E-mail: manufl{at}usc.es


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