η-Ricci Solitons on Sasakian 3-Manifolds

Majhi, Pradip; De, Uday Chand; Kar, Debabrata

doi:10.1515/awutm-2017-0019

Abstract

In this paper we study η-Ricci solitons on Sasakian 3-manifolds. Among others we prove that an η-Ricci soliton on a Sasakian 3-manifold is an η-Einstien manifold. Moreover we consider η-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat and φ-Ricci symmetric η-Ricci soliton on Sasakian 3-manifolds. Also η-Ricci soliton on Sasakian 3-manifolds with the curvature condition Q.R = 0 have been considered. Finally, we construct an example to prove the non-existence of proper η-Ricci solitons on Sasakian 3-manifolds and verify some results.

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η-Ricci Solitons on Sasakian 3-Manifolds

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