1
Department of Pure Mathematics, University of Calcutta, India.
2
Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, West Bengal, India
10.22034/kjm.2020.235131.1873
Abstract
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 $h'$.
Dey, D., & Majhi, P. (2021). Almost Kenmotsu manifolds admitting certain vector fields. Khayyam Journal of Mathematics, 7(2), 310-320. doi: 10.22034/kjm.2020.235131.1873
Dey, D., Majhi, P. (2021). 'Almost Kenmotsu manifolds admitting certain vector fields', Khayyam Journal of Mathematics, 7(2), pp. 310-320. doi: 10.22034/kjm.2020.235131.1873
VANCOUVER
Dey, D., Majhi, P. Almost Kenmotsu manifolds admitting certain vector fields. Khayyam Journal of Mathematics, 2021; 7(2): 310-320. doi: 10.22034/kjm.2020.235131.1873
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