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This article is cited in 9 scientific papers (total in 9 papers)
Ricci solitons and certain related metrics on almost co-Kaehler manifolds
Devaraja Mallesha Naika, V. Venkateshab, H. Aruna Kumarab a Department of Mathematics, CHRIST (Deemed to be University), Bengaluru-560029, Karnataka, India
b Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka 577 451, India
Abstract:
In the paper, we study a Ricci soliton and a generalized $m$-quasi-Einstein metric on almost co-Kaehler manifold $M$ satisfying a nullity condition. First, we consider a non-co-Kaehler $(\kappa, \mu)$-almost co-Kaehler metric as a Ricci soliton and prove that the soliton is expanding with $\lambda=-2n\kappa$ and the soliton vector field $X$ leaves the structure tensors $\eta,\xi$ and $\varphi$ invariant. This result extends Theorem 5.1 of [32]. We construct an example to show the existence of a Ricci soliton on $M$. Finally, we prove that if $M$ is a generalized $(\kappa, \mu)$-almost co-Kaehler manifold of dimension higher than 3 such that $h\neq 0$, then the metric of $M$ can not be a generalized $m$-quasi-Einstein metric, and this recovers the recent result of Wang [37, Theorem 4.1] as a special case.
Key words and phrases:
almost co-Kaehler manifold, Ricci soliton, generalized $m$-quasi-Einstein metric, $(\kappa, \mu)$-nullity distribution.
Received: 11.11.2019 Revised: 01.04.2020
Citation:
Devaraja Mallesha Naik, V. Venkatesha, H. Aruna Kumara, “Ricci solitons and certain related metrics on almost co-Kaehler manifolds”, Zh. Mat. Fiz. Anal. Geom., 16:4 (2020), 402–417
Linking options:
https://www.mathnet.ru/eng/jmag764 https://www.mathnet.ru/eng/jmag/v16/i4/p402
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