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Annals of Global Analysis and Geometry

, Volume 42, Issue 2, pp 195–205 | Cite as

Remarks on scalar curvature of Yamabe solitons

  • Li MaEmail author
  • Vicente Miquel
Article

Abstract

In this article, we consider the scalar curvature of Yamabe solitons. In particular, we show that, with natural conditions and non-positive Ricci curvature, any complete Yamabe soliton has constant scalar curvature, namely, it is a Yamabe metric. We also show that a complete non-compact Yamabe soliton with the quadratic decay at infinity of its Ricci curvature has non-negative scalar curvature. A new proof of Kazdan–Warner condition is also presented.

Keywords

Yamabe solitons Constant scalar curvature metric 

Mathematics Subject Classification (2000)

35Jxx 53Cxx 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsHenan Normal UniversityXinxiangChina
  2. 2.Department of Geometry and TopologyUniversity of ValenciaBurjassotSpain

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