Remarks on scalar curvature of Yamabe solitons
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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.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2ee0a826aa21be842cfbfa3819633df5037e4dda