Kenmotsu 3-metric as a Ricci soliton

We show that, if a 3-dimensional Kenmotsu metric is a Ricci soliton then it is of constant curvature −1 and the soliton is expanding.

► We consider Kenmotsu 3-metric as a Ricci soliton and prove that it is of constant curvature −1.
► In this case the soliton is expanding.
► There exists such a metric on the warped product of a Riemann surface with the real line.