Almost \(\eta \)-Ricci solitons on Kenmotsu manifolds (Q2667156)

In the paper under review the Einstein metrics are studied as almost \(\eta\)-Ricci solitons and \(\eta\)-Ricci solitons on Kenmotsu manifolds. The authors prove that a Kenmotsu metric as an \(\eta\)-Ricci soliton is Einstein metric if either it is \(\eta\)-Einstein or the potential vector field is an infinitesimal contact transformation or the potential vector field is collinear to the Reeb vector field. Also, it is shown that if a Kenmotsu manifold admits a gradient almost \(\eta\)-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then it is an Einstein manifold. New examples of \(\eta\)-Ricci solitons and gradient \(\eta\)-Ricci solitons are presented. Some interesting open questions are listed at the end of the paper.