TY - JOUR ID - 131347 TI - Almost Kenmotsu manifolds admitting certain vector fields JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Dey, Dibakar AU - Majhi, Pradip AD - Department of Pure Mathematics, University of Calcutta, India. AD - Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India Y1 - 2021 PY - 2021 VL - 7 IS - 2 SP - 310 EP - 320 KW - Almost Kenmotsu manifold KW - Holomorphically Planar conformal vector field KW - Almost Kaehler manifold KW - Totally umbilical submanifolds DO - 10.22034/kjm.2020.235131.1873 N2 - 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 $h'$. UR - https://www.kjm-math.org/article_131347.html L1 - https://www.kjm-math.org/article_131347_bdd8045bc7b7de265443a172ec53739b.pdf ER -