$m$-quasi-$*$-Einstein contact metric manifolds
The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta$-Einstein and $f$ is constant. Next, we show that in...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2022-04-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4736 |
| _version_ | 1797205781349662720 |
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| author | H.A. Kumara V. Venkatesha D.M. Naik |
| author_facet | H.A. Kumara V. Venkatesha D.M. Naik |
| author_sort | H.A. Kumara |
| collection | DOAJ |
| description | The goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta$-Einstein and $f$ is constant. Next, we show that in a Sasakian manifold if $g$ represents an $m$-quasi-$*$-Einstein metric with a conformal vector field $V$, then $V$ is Killing and $M$ is $\eta$-Einstein. Finally, we prove that if a non-Sasakian $(\kappa,\mu)$-contact manifold admits a gradient $m$-quasi-$*$-Einstein metric, then it is $N(\kappa)$-contact metric manifold or a $*$-Einstein. |
| first_indexed | 2024-04-24T08:56:34Z |
| format | Article |
| id | doaj.art-26de9846c2dc428c9df84db90643521d |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:34Z |
| publishDate | 2022-04-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-26de9846c2dc428c9df84db90643521d2024-04-16T07:10:59ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102022-04-01141617110.15330/cmp.14.1.61-714128$m$-quasi-$*$-Einstein contact metric manifoldsH.A. Kumara0https://orcid.org/0000-0002-4714-3063V. Venkatesha1https://orcid.org/0000-0002-2799-2535D.M. Naik2Kuvempu University, Shankaraghatta, 577451, Karnataka, IndiaKuvempu University, Shankaraghatta, 577451, Karnataka, IndiaCHRIST (Deemed to be University), Bangalore, 560029, Karnataka, IndiaThe goal of this article is to introduce and study the characterstics of $m$-quasi-$*$-Einstein metric on contact Riemannian manifolds. First, we prove that if a Sasakian manifold admits a gradient $m$-quasi-$*$-Einstein metric, then $M$ is $\eta$-Einstein and $f$ is constant. Next, we show that in a Sasakian manifold if $g$ represents an $m$-quasi-$*$-Einstein metric with a conformal vector field $V$, then $V$ is Killing and $M$ is $\eta$-Einstein. Finally, we prove that if a non-Sasakian $(\kappa,\mu)$-contact manifold admits a gradient $m$-quasi-$*$-Einstein metric, then it is $N(\kappa)$-contact metric manifold or a $*$-Einstein.https://journals.pnu.edu.ua/index.php/cmp/article/view/4736$*$-ricci soliton$m$-quasi-$*$-einstein metricsasakian manifold$(\kappa,\mu)$-contact manifold |
| spellingShingle | H.A. Kumara V. Venkatesha D.M. Naik $m$-quasi-$*$-Einstein contact metric manifolds Karpatsʹkì Matematičnì Publìkacìï $*$-ricci soliton $m$-quasi-$*$-einstein metric sasakian manifold $(\kappa,\mu)$-contact manifold |
| title | $m$-quasi-$*$-Einstein contact metric manifolds |
| title_full | $m$-quasi-$*$-Einstein contact metric manifolds |
| title_fullStr | $m$-quasi-$*$-Einstein contact metric manifolds |
| title_full_unstemmed | $m$-quasi-$*$-Einstein contact metric manifolds |
| title_short | $m$-quasi-$*$-Einstein contact metric manifolds |
| title_sort | m quasi einstein contact metric manifolds |
| topic | $*$-ricci soliton $m$-quasi-$*$-einstein metric sasakian manifold $(\kappa,\mu)$-contact manifold |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/4736 |
| work_keys_str_mv | AT hakumara mquasieinsteincontactmetricmanifolds AT vvenkatesha mquasieinsteincontactmetricmanifolds AT dmnaik mquasieinsteincontactmetricmanifolds |