<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper we study <italic>η</italic>-Ricci solitons on Sasakian 3-manifolds. Among others we prove that an <italic>η</italic>-Ricci soliton on a Sasakian 3-manifold is an <italic>η</italic>-Einstien manifold. Moreover we consider <italic>η</italic>-Ricci solitons on Sasakian 3-manifolds with Ricci tensor of Codazzi type and cyclic parallel Ricci tensor. Beside these we study conformally flat and <italic>φ</italic>-Ricci symmetric <italic>η</italic>-Ricci soliton on Sasakian 3-manifolds. Also <italic>η</italic>-Ricci soliton on Sasakian 3-manifolds with the curvature condition <italic>Q.R</italic> = 0 have been considered. Finally, we construct an example to prove the non-existence of proper <italic>η</italic>-Ricci solitons on Sasakian 3-manifolds and verify some results.</p></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.

<italic>η</italic>-Ricci Solitons on Sasakian 3-Manifolds

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":{"italic":"η","content":"-Ricci Solitons on Sasakian 3-Manifolds"}}

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...

η-Ricci Solitons on Sasakian 3-Manifolds

Published Online: Dec 29, 2017

Page range: 143 - 156

Received: Aug 25, 2017

Accepted: Oct 08, 2017

DOI: https://doi.org/10.1515/awutm-2017-0019

Keywords
Ricci soliton, -Ricci soliton, Sasakian 3-manifolds, Ricci tensor of Coddazi type, cyclic parallel Ricci tensor

© 2017 Pradip Majhi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

η-Ricci Solitons on Sasakian 3-Manifolds

Published Online: Dec 29, 2017

Page range: 143 - 156

Received: Aug 25, 2017

Accepted: Oct 08, 2017

DOI: https://doi.org/10.1515/awutm-2017-0019

KeywordsRicci soliton, -Ricci soliton, Sasakian 3-manifolds, Ricci tensor of Coddazi type, cyclic parallel Ricci tensor

© 2017 Pradip Majhi et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Ricci soliton, -Ricci soliton, Sasakian 3-manifolds, Ricci tensor of Coddazi type, cyclic parallel Ricci tensor