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.
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Ma, L., Miquel, V. Remarks on scalar curvature of Yamabe solitons. Ann Glob Anal Geom 42, 195–205 (2012). https://doi.org/10.1007/s10455-011-9308-7
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DOI: https://doi.org/10.1007/s10455-011-9308-7