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Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold
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| Zeitschriftentitel: | Carpathian Mathematical Publications |
|---|---|
| Personen und Körperschaften: | |
| In: | Carpathian Mathematical Publications, 11, 2019, 1, S. 59-69 |
| Format: | E-Article |
| Sprache: | Unbestimmt |
| veröffentlicht: |
Vasyl Stefanyk Precarpathian National University
|
| Schlagwörter: |
| author_facet |
Ghosh, A. Ghosh, A. |
|---|---|
| author |
Ghosh, A. |
| spellingShingle |
Ghosh, A. Carpathian Mathematical Publications Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold General Mathematics |
| author_sort |
ghosh, a. |
| spelling |
Ghosh, A. 2313-0210 2075-9827 Vasyl Stefanyk Precarpathian National University General Mathematics http://dx.doi.org/10.15330/cmp.11.1.59-69 <jats:p>First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.</jats:p> Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold Carpathian Mathematical Publications |
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Carpathian Mathematical Publications |
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| title |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_unstemmed |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_full |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_fullStr |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_full_unstemmed |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_short |
Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_sort |
ricci soliton and ricci almost soliton within the framework of kenmotsu manifold |
| topic |
General Mathematics |
| url |
http://dx.doi.org/10.15330/cmp.11.1.59-69 |
| publishDate |
2019 |
| physical |
59-69 |
| description |
<jats:p>First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.</jats:p> |
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| description | <jats:p>First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.</jats:p> |
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| imprint | Vasyl Stefanyk Precarpathian National University, 2019 |
| imprint_str_mv | Vasyl Stefanyk Precarpathian National University, 2019 |
| institution | DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275 |
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| physical | 59-69 |
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| publisher | Vasyl Stefanyk Precarpathian National University |
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| recordtype | ai |
| series | Carpathian Mathematical Publications |
| source_id | 49 |
| spelling | Ghosh, A. 2313-0210 2075-9827 Vasyl Stefanyk Precarpathian National University General Mathematics http://dx.doi.org/10.15330/cmp.11.1.59-69 <jats:p>First, we prove that if the Reeb vector field $\xi$ of a Kenmotsu manifold $M$ leaves the Ricci operator $Q$ invariant, then $M$ is Einstein. Next, we study Kenmotsu manifold whose metric represents a Ricci soliton and prove that it is expanding. Moreover, the soliton is trivial (Einstein) if either (i) $V$ is a contact vector field, or (ii) the Reeb vector field $\xi$ leaves the scalar curvature invariant. Finally, it is shown that if the metric of a Kenmotsu manifold represents a gradient Ricci almost soliton, then it is $\eta$-Einstein and the soliton is expanding. We also exhibited some examples of Kenmotsu manifold that admit Ricci almost solitons.</jats:p> Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold Carpathian Mathematical Publications |
| spellingShingle | Ghosh, A., Carpathian Mathematical Publications, Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold, General Mathematics |
| title | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_full | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_fullStr | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_full_unstemmed | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_short | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| title_sort | ricci soliton and ricci almost soliton within the framework of kenmotsu manifold |
| title_unstemmed | Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold |
| topic | General Mathematics |
| url | http://dx.doi.org/10.15330/cmp.11.1.59-69 |