Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry
The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k<-1$ or $k>-1$ and whose potential vector field is th...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2019-07-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/33027 |
| _version_ | 1811259536487481344 |
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| author | Uday Chand De Krishanu Mandal |
| author_facet | Uday Chand De Krishanu Mandal |
| author_sort | Uday Chand De |
| collection | DOAJ |
| description | The purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k<-1$ or $k>-1$ and whose potential vector field is the Reeb vector field $\xi$. Further, if the metric $g$ of a $(k,\mu)$-paracontact metric manifold $M^{2n+1}$ with $k\neq-1$ is a gradient Ricci almost soliton, then we prove either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or, $M^{2n+1}$ is an Einstein manifold. |
| first_indexed | 2024-04-12T18:33:05Z |
| format | Article |
| id | doaj.art-76b0ad8fa428464d8926aa26fe9d87b0 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-04-12T18:33:05Z |
| publishDate | 2019-07-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-76b0ad8fa428464d8926aa26fe9d87b02022-12-22T03:21:01ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882019-07-0137311913010.5269/bspm.v37i3.3302717309Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometryUday Chand De0Krishanu Mandal1University of Calcutta Department of Pure MathematicsUniversity of Calcutta Department of Pure MathematicsThe purpose of this paper is to study Ricci almost soliton and gradient Ricci almost soliton in $(k,\mu)$-paracontact metric manifolds. We prove the non-existence of Ricci almost soliton in a $(k,\mu)$-paracontact metric manifold $M$ with $k<-1$ or $k>-1$ and whose potential vector field is the Reeb vector field $\xi$. Further, if the metric $g$ of a $(k,\mu)$-paracontact metric manifold $M^{2n+1}$ with $k\neq-1$ is a gradient Ricci almost soliton, then we prove either the manifold is locally isometric to a product of a flat $(n+1)$-dimensional manifold and an $n$-dimensional manifold of negative constant curvature equal to $-4$, or, $M^{2n+1}$ is an Einstein manifold.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/33027$(k,\mu)$-paracontact manifoldRicci almost solitonGradient Ricci almost solitonEinstein manifold |
| spellingShingle | Uday Chand De Krishanu Mandal Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry Boletim da Sociedade Paranaense de Matemática $(k,\mu)$-paracontact manifold Ricci almost soliton Gradient Ricci almost soliton Einstein manifold |
| title | Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry |
| title_full | Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry |
| title_fullStr | Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry |
| title_full_unstemmed | Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry |
| title_short | Ricci almost solitons and gradient Ricci almost solitons in $(k,\mu)$-paracontact geometry |
| title_sort | ricci almost solitons and gradient ricci almost solitons in k mu paracontact geometry |
| topic | $(k,\mu)$-paracontact manifold Ricci almost soliton Gradient Ricci almost soliton Einstein manifold |
| url | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/33027 |
| work_keys_str_mv | AT udaychandde riccialmostsolitonsandgradientriccialmostsolitonsinkmuparacontactgeometry AT krishanumandal riccialmostsolitonsandgradientriccialmostsolitonsinkmuparacontactgeometry |