Almost Kenmotsu manifolds admitting certain vector fields

D. Dey, P. Majhi
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Abstract

In the present paper, we characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields. We have shown that if an almost Kenmotsu manifold $M^{2n+1}$ admits a non-zero HPCV field $V$ such that $\phi V = 0$, then $M^{2n+1}$ is locally a warped product of an almost Kaehler manifold and an open interval. As a corollary of this we obtain few classifications of an almost Kenmotsu manifold to be a Kenmotsu manifold and also prove that the integral manifolds of D are totally umbilical submanifolds of $M^{2n+1}$. Further, we prove that if an almost Kenmotsu manifold with positive constant $\xi$-sectional curvature admits a non-zero HPCV field $V$, then either $M^{2n+1}$ is locally a warped product of an almost Kaehler manifold and an open interval or isometric to a sphere. Moreover, a $(k,\mu)'$-almost Kenmotsu manifold admitting a HPCV field $V$ such that $\phi V = 0$ is either locally isometric to $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$ or $V$ is an eigenvector of $h'$. Finally, an example is presented.
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几乎Kenmotsu流形承认某些向量场
在本文中,我们刻画了具有全纯平面共形矢量场的几乎Kenmotsu流形。我们证明了如果一个几乎Kenmotsu流形$M^{2n+1}$允许一个非零HPCV场$V$使得$\phi V = 0$,那么$M^{2n+1}$是一个几乎Kaehler流形与开区间的局部翘曲积。作为这一结论的推论,我们得到了几乎Kenmotsu流形为Kenmotsu流形的几个分类,并证明了D的积分流形是$M^{2n+1}$的完全脐带子流形。进一步证明了如果一个具有正常数$\xi$ -截面曲率的几乎Kenmotsu流形存在一个非零HPCV场$V$,那么$M^{2n+1}$要么是一个几乎Kaehler流形与球面的开区间或等距的局部翘曲积。此外,承认HPCV场$V$的$(k,\mu)'$ -几乎Kenmotsu流形使得$\phi V = 0$与$\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$局部等距或$V$是$h'$的特征向量。最后给出了一个实例。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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