Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry
We prove that if an -Einstein para-Kenmotsu manifold admits a conformal -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal -Ricci soliton is Einstein if its potential vector field is infinitesimal paracontact transformation or collinear with the Reeb vecto...
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| Published in | Open mathematics (Warsaw, Poland) Vol. 20; no. 1; pp. 574 - 589 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Warsaw
De Gruyter
09.08.2022
De Gruyter Poland |
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| Abstract | We prove that if an
-Einstein para-Kenmotsu manifold admits a conformal
-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal
-Ricci soliton is Einstein if its potential vector field
is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal
-Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal
-Ricci soliton and satisfy our results. We also have studied conformal
-Ricci soliton in three-dimensional para-cosymplectic manifolds. |
|---|---|
| AbstractList | We prove that if an η-Einstein para-Kenmotsu manifold admits a conformal η-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η-Ricci soliton is Einstein if its potential vector field V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η-Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η-Ricci soliton and satisfy our results. We also have studied conformal η-Ricci soliton in three-dimensional para-cosymplectic manifolds. We prove that if an -Einstein para-Kenmotsu manifold admits a conformal -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal -Ricci soliton is Einstein if its potential vector field is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal -Ricci soliton and satisfy our results. We also have studied conformal -Ricci soliton in three-dimensional para-cosymplectic manifolds. We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds. We prove that if an η\eta -Einstein para-Kenmotsu manifold admits a conformal η\eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η\eta -Ricci soliton is Einstein if its potential vector field VV is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η\eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η\eta -Ricci soliton and satisfy our results. We also have studied conformal η\eta -Ricci soliton in three-dimensional para-cosymplectic manifolds. |
| Author | Li, Yanlin Ali, Akram Dey, Santu Pahan, Sampa |
| Author_xml | – sequence: 1 givenname: Yanlin surname: Li fullname: Li, Yanlin email: liyl@hznu.edu.cn organization: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China – sequence: 2 givenname: Santu surname: Dey fullname: Dey, Santu email: santu.mathju@gmail.com organization: Department of Mathematics, Bidhan Chandra College, Asansol 713304, India – sequence: 3 givenname: Sampa surname: Pahan fullname: Pahan, Sampa email: sampapahan25@gmail.com organization: Department of Mathematics, Mrinalini Datta Mahavidyapith, Kolkata 700 051, India – sequence: 4 givenname: Akram surname: Ali fullname: Ali, Akram email: akramali133@gmail.com organization: Department of Mathematics, College of Science, King Khalid University, 61421 Abha, Saudi Arabia |
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| Snippet | We prove that if an
-Einstein para-Kenmotsu manifold admits a conformal
-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a... We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu... We prove that if an η-Einstein para-Kenmotsu manifold admits a conformal η-Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a... We prove that if an η\eta -Einstein para-Kenmotsu manifold admits a conformal η\eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu... |
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| StartPage | 574 |
| SubjectTerms | 53C15 53C25 53D15 conformal η-Ricci soliton Einstein manifold Fields (mathematics) infinitesimal contact transformation Kenmotsu manifold Manifolds (mathematics) para-cosymplectic manifold Solitary waves |
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| Title | Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry |
| URI | https://www.degruyter.com/doi/10.1515/math-2022-0048 https://www.proquest.com/docview/2700011854 https://doaj.org/article/47c92c2f9b984806b366ac34491c0713 |
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