Some remarks on Yamabe solitons

2018/03/14 by Chakraborty, Debabrata, Mandal, Yadab Chandra, Hui, Shyamal Kumar
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.05204

Abstract

In this paper we have obtained evolution of some geometric quantities on a compact Riemannian manifold Mⁿ when the metric is a Yamabe soliton. Using these quantities we have obtained bound on the soliton constant. We have proved that the commutator of two soliton vector fields with the same metric in a given conformal class produces a Killing vector field. Also it is shown that the soliton vector field becomes a geodesic vector field if and only if the manifold is of constant curvature.

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