\( \eta \)-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds

  • Sampa Pahan Department of Mathematics, Mrinalini Datta Mahavidyapith Kolkata-700051, India.
Keywords: Trans-Sasakian manifold, η-Ricci solitons

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 \(S \cdot W_2 = 0\).

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Published
2020-04-17
How to Cite
Pahan, S. (2020). \( \eta \)-Ricci Solitons on 3-dimensional Trans-Sasakian Manifolds. CUBO, A Mathematical Journal, 22(1), 23–37. https://doi.org/10.4067/S0719-06462020000100023