$m$-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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 2075-9827 2313-0210 |