\( \eta \)-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds
Author
Pahan, Sampa
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/225410.4067/S0719-06462020000100023
Abstract
In this paper, we study \( \eta \)-Ricci solitons on 3-dimensional trans-Sasakian manifolds. Firstly we give conditions for the existence of these geometric structures and then observe that they provide examples of \( \eta \)-Einstein manifolds. In the case of \( \phi \)-Ricci symmetric trans-Sasakian manifolds, the η-Ricci soliton condition turns them to Einstein manifolds. Afterward, we study the implications in this geometric context of the important tensorial conditions \( R \cdot S = 0\), \(S \cdot R = 0\), \(W_2\cdot S = 0\) and \(S \cdot W_2 = 0\).