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arxiv: 1810.13020 · v1 · pith:IBMWRH57new · submitted 2018-10-30 · 🧮 math.DG · math.AP

Conformal vector fields and Yamabe solitons

classification 🧮 math.DG math.AP
keywords metricsyamabeconditionsfieldssolitonsvectorconformalsufficient
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In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar curvature. More precisely, we use properties of conformal vector fields to find several sufficient conditions on the soliton vector fields of Yamabe solitons under which their metrics are of Yamabe metrics.

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