<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The object of the present paper is to study Ricci soliton in <italic>β</italic>-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a <italic>β</italic>-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒ<italic>Vg</italic> +2<italic>S</italic>)is ∇-parallel where <italic>V</italic> is a given vector field, then the structure (<italic>g, V, λ</italic>) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in <italic>β</italic>-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional <italic>β</italic>-Kenmotsu manifold are discussed with an example.</p></abstract>

The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in a β-Kenmotsu manifold is a constant multiple of the metric tensor. Using this result, it is shown that if (ℒVg +2S)is ∇-parallel where V is a given vector field, then the structure (g, V, λ) yields a Ricci soliton. Further, by virtue of this result, we found the conditions of Ricci soliton in β-Kenmotsu manifold to be shrinking, steady and expending respectively. Next, Ricci soliton for 3-dimensional β-Kenmotsu manifold are discussed with an example.

Ricci Solitons in <italic>β</italic>-Kenmotsu 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":"β","content":["Ricci Solitons in","-Kenmotsu Manifolds"]}}

The object of the present paper is to study Ricci soliton in β-Kenmotsu manifolds. Here it is proved that a symmetric parallel second order covariant tensor in...

Ricci Solitons in β-Kenmotsu Manifolds

Published Online: Dec 07, 2018

Page range: 149 - 163

Received: Jan 31, 2017

Accepted: Jul 22, 2018

DOI: https://doi.org/10.2478/awutm-2018-0010

Keywords
Ricci flow, Ricci soliton, -Kenmotsu manifold, Einstein manifold

© 2018 Rajesh Kumar, published by Sciendo

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

Ricci Solitons in β-Kenmotsu Manifolds

Published Online: Dec 07, 2018

Page range: 149 - 163

Received: Jan 31, 2017

Accepted: Jul 22, 2018

DOI: https://doi.org/10.2478/awutm-2018-0010

KeywordsRicci flow, Ricci soliton, -Kenmotsu manifold, Einstein manifold

© 2018 Rajesh Kumar, published by Sciendo

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

Keywords
Ricci flow, Ricci soliton, -Kenmotsu manifold, Einstein manifold