%0 Journal Article %T Almost Kenmotsu manifolds admitting certain vector fields %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Dey, Dibakar %A Majhi, Pradip %D 2021 %\ 07/01/2021 %V 7 %N 2 %P 310-320 %! Almost Kenmotsu manifolds admitting certain vector fields %K Almost Kenmotsu manifold %K Holomorphically Planar conformal vector field %K Almost Kaehler manifold %K Totally umbilical submanifolds %R 10.22034/kjm.2020.235131.1873 %X The object of the present paper is to characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (in short, HPCV) fields. It is shown that an almost Kenmotsu manifold $M^{2n+1}$ admitting a non-zero HPCV field $V$ such that $V$ is pointwise collinear with the Reeb vector field $\xi$ is locally a warped product of an almost Kaehler manifold and an open interval. Further, if an almost Kenmotsu manifold with constant $\xi$-sectional curvature admits a non-zero HPCV field $V$, then $M^{2n+1}$ is locally a warped product of an almost Kaehler manifold and an open interval. Moreover, a $(k,\mu)'$-almost Kenmotsu manifold admitting a HPCV field $V$ such that $\phi V \neq 0$ is either locally isometric to $\mathbb{H}^{n+1}(-4)$ $\times$ $\mathbb{R}^n$ or $V$ is an eigenvector of $h'$. %U https://www.kjm-math.org/article_131347_bdd8045bc7b7de265443a172ec53739b.pdf