RICCI SOLITONS ON THREE-DIMENSIONAL $\eta$-EINSTEIN ALMOST KENMOTSU MANIFOLDS

Abstract

Let the metric $g$ of a three-dimensional $\eta$-Einstein almost Kenmotsu manifold $M$ be a Ricci soliton, we prove that $M$ is a Kenmotsu manifold of constant sectional curvature $-1$ and the soliton is expanding.