On a class of complete non-compact gradient Yamabe solitons
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 851-863
Published online May 31, 2018
Jia-Yong Wu
Shanghai Maritime University
Abstract : We derive lower bounds of the scalar curvature on complete non-compact gradient Yamabe solitons under some integral curvature conditions. Based on this, we prove that potential functions of Yamabe solitons have at most quadratic growth for distance function. We also obtain a finite topological type property on complete shrinking gradient Yamabe solitons under suitable scalar curvature assumptions.
Keywords : Yamabe flow, Yamabe soliton, self-similar solution, finite topological type
MSC numbers : Primary 53C21; Secondary 53C44, 55Q52
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