Remarks on scalar curvature of Yamabe solitons |
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Authors: | Li Ma Vicente Miquel |
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Affiliation: | 1. Department of Mathematics, Henan Normal University, Xinxiang, 453007, China 2. Department of Geometry and Topology, University of Valencia, Av. Vicent Andr??s EsteII??s 1, 46100, Burjassot, Valencia, Spain
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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?CWarner condition is also presented. |
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