2011/09/11 by He, Chenxu
#53C25 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1109.2343
The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\citeCaoSunZhang shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational symmetry, or on the warped product of the real line with a manifold of constant scalar curvature. In this paper we consider the classification in the latter case. We show that a complete gradient steady Yamabe soliton on warped product is necessarily isometric to the Riemannian product. In the shrinking case, we show that there is a continuous family of complete gradient Yamabe shrinkers on warped products which are not isometric to the Riemannian product in dimension three and higher.