Gradient Yamabe solitons with conformal vector field
Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 165-171 https://doi.org/10.4134/CKMS.c200104 Published online November 12, 2020 Printed January 31, 2021
Ghodratallah Fasihi-Ramandi, Hajar Ghahremani-Gol Imam Khomeini International University; Shahed University
Abstract : The purpose of this paper is to investigate the geometry of complete gradient Yamabe soliton $(M^n ,g, f, \lambda)$ with constant scalar curvature admitting a non-homothetic conformal vector field $V$ leaving the potential vector field invariant. We show that in such manifolds the potential function $f$ is constant and the scalar curvature of $g$ is determined by its soliton scalar. Considering the locally conformally flat case and conformal vector field $V$, without constant scalar curvature assumption, we show that $g$ has constant curvature and determines the potential function $f$ explicitly.
Keywords : Yamabe soliton, constant scalar curvature, conformal vector field
