Remarks on scalar curvature of Yamabe solitons

Details Remarks on scalar curvature of Yamabe solitons Remarks on scalar curvature of Yamabe solitons

2011-08-31

arxiv.org/abs/1108.6212v1

Mathematics

Differential Geometry

10 pages

Scientific paper

In this paper, 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 the quadratic decay at infinity of the Ricci curvature of a complete non-compact Yamabe soliton has non-negative scalar curvature. A new proof of Kazdan-Warner condition is also presented.

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