<i>η</i>-∗-Ricci Solitons and Almost co-Kähler Manifolds

Abstract

The subject of the present paper is the investigation of a new type of solitons, called η-∗-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on ackm is obtained. Additionally, we classify the η-∗-Ricci solitons in (k,μ)-ackms. Next, we investigate (k,μ)-ackms admitting gradient η-∗-Ricci solitons. Finally, we construct two examples to illustrate our results.

Keywords

• ∗-Ricci tensor
• <i>η</i>-∗-Ricci solitons
• gradient <i>η</i>-∗-Ricci solitons
• almost co-Kähler manifolds
• (<i>k</i>,<i>μ</i>)-almost co-Kähler manifolds