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On gradient Ricci solitons with constant scalar curvature


Authors: Manuel Fernández-López and Eduardo García-Río
Journal: Proc. Amer. Math. Soc. 144 (2016), 369-378
MSC (2010): Primary 53C25, 53C20, 53C44
DOI: https://doi.org/10.1090/proc/12693
Published electronically: June 26, 2015
MathSciNet review: 3415603
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Abstract: We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which are all satisfied if the manifold is curvature homogeneous. This leads to a complete description of four- and six-dimensional Kähler gradient Ricci solitons with constant scalar curvature.


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Additional Information

Manuel Fernández-López
Affiliation: IES María Sarmiento, Consellería de Educación, Xunta de Galicia, Lugo, Spain
Email: manufl@edu.xunta.es

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

DOI: https://doi.org/10.1090/proc/12693
Keywords: Gradient Ricci soliton, scalar curvature.
Received by editor(s): September 17, 2014
Received by editor(s) in revised form: December 12, 2014
Published electronically: June 26, 2015
Additional Notes: The authors were supported by projects GRC2013-045 and MTM2013-41335-P with FEDER funds (Spain)
Communicated by: Guofang Wei
Article copyright: © Copyright 2015 American Mathematical Society