A study of conformal almost Ricci solitons on Kenmotsu manifolds
The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is η -Einstein Kenmots...
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| Published in | International journal of geometric methods in modern physics Vol. 20; no. 4 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Singapore
World Scientific Publishing Company
30.03.2023
World Scientific Publishing Co. Pte., Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0219-8878 1793-6977 |
| DOI | 10.1142/S0219887823300015 |
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| Abstract | The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is
η
-Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of
λ
is pointwise collinear with the Reeb vector field or the manifold becomes
η
-Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold. |
|---|---|
| AbstractList | The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is η-Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of λ is pointwise collinear with the Reeb vector field or the manifold becomes η-Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold. The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is η -Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of λ is pointwise collinear with the Reeb vector field or the manifold becomes η -Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold. The goal of this paper is to study conformal almost Ricci solitons within the framework of Kenmotsu manifolds. First, we demonstrate that if the potential vector field is Jacobi along the Reeb vector field, then the soliton reduces to a conformal Ricci soliton. If the manifold is [Formula: see text]-Einstein Kenmotsu manifold, we show that either the manifold is of constant scalar curvature or the potential vector field is an infinitesimal contact transformation. In addition, if we consider the soliton vector field as a contact vector field, then either the gradient of [Formula: see text] is pointwise collinear with the Reeb vector field or the manifold becomes [Formula: see text]-Einstein. Lastly, we develop an example of a conformal almost Ricci soliton on the Kenmotsu manifold. |
| Author | Dey, Santu Sarkar, Sumanjit Bhattacharyya, Arindam |
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| Cites_doi | 10.1007/s40065-019-00269-7 10.1515/ms-2017-0321 10.1515/ms-2017-0026 10.1142/0069 10.1142/S0129167X95000110 10.1007/s00605-014-0657-8 10.1016/j.geomphys.2016.12.010 10.3390/math8091592 10.2996/kmj/1138036310 10.1007/s00013-013-0524-1 10.2748/tmj/1178241594 10.1090/conm/071/954419 10.2748/tmj/1178243031 10.2298/FIL2115001S 10.1017/S0017089514000494 10.1007/978-0-8176-4959-3 10.1088/0264-9381/21/3/011 10.1016/j.geomphys.2021.104339 |
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| Keywords | Ricci flow conformal Ricci flow Kenmotsu manifold conformal almost Ricci soliton |
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| Title | A study of conformal almost Ricci solitons on Kenmotsu manifolds |
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