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Almost Kenmotsu manifolds admitting certain vector fields
Dibakar Dey,Pradip Majhi +1 more
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In this article, the authors characterized almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields and showed that the integral manifolds of D are totally umbilical submanifolds of an almost Kaehler manifold.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.read more
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Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday
A Note on Two Classes of $\xi$-Conformally Flat Almost Kenmotsu Manifolds
TL;DR: In this article, it was shown that a 2n+1-dimensional manifold is conformally flat if and only if it is an Einstein manifold and if the manifold is an almost Kenmotsu manifold.
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Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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Almost Kenmotsu manifolds and local symmetry
Giulia Dileo,Anna Maria Pastore +1 more
TL;DR: In this paper, the authors consider locally symmetric almost Kenmotsu manifold and show that the manifold is locally isometric to the Riemannian product of an n+1-dimensional manifold of constant curvature.
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Almost Kenmotsu Manifolds and Nullity Distributions
Giulia Dileo,Anna Maria Pastore +1 more
TL;DR: In this paper, the authors characterize almost contact metric manifolds which are CR-integrable almost Kenmotsu, through the existence of a suitable linear connection, and give examples and completely describe the three dimensional case.