The purpose of this paper is to investigate the Fischer-Marsden conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional non-Kenmotsu (k, µ)′-almost Kenmotsu manifold sa...

The Fischer-Marsden conjecture on almost Kenmotsu manifolds

We study the critical point equation $(CPE)$ conjecture on almost Kenmotsu manifolds. First, we prove that if a three-dimensional $(k,\mu)'$-almost Kenmotsu manifold satisfies the $CPE,$ then the manifold is either locally isometric to the product space $\mathbb H^2(-4)\times\mathbb R$ or the manifold is Kenmotsu manifold. Further, we prove that if the metric of an almost Kenmotsu manifold with conformal Reeb foliation satisfies the $CPE$ conjecture, then the manifold is Einstein.

Critical Point Equation on Almost Kenmotsu Manifolds

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with  $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

/pdf/on-the-quasi-conformal-curvature-tensor-of-an-almost-3v0ktvw5xm.pdf

On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

In the present paper, we prove that if the metric of a three dimensional almost Kenmotsu manifold with $\textbf{Q}\phi=\phi \textbf{Q}$ whose scalar curvature remains invariant under the chracterstic vector field $\zeta$, admits a non-trivial Yamabe solitons, then the manifold is of constant sectional curvature or the manifold is Ricci simple.

https://dergipark.org.tr/en/download/article-file/2904321

A Note on Yamabe Solitons on 3-dimensional Almost Kenmotsu Manifolds with $\textbf{Q}\phi=\phi \textbf{Q}$

In this short note we prove that there does not exist Ricci soliton $(g,\xi )$ in an almost Kenmotsu manifold.

Non-existence of Ricci solitons in almost Kenmotsu manifolds

The purpose of this paper is to investigate φ-Ricci recurrent and φ-Ricci symmetric almost Kenmotsu manifolds with its characteristic vector field ξ belonging to some nullity distributions. Also we obtain several corollaries. Finally, we give an example of a 5-dimensional almost Kenmotsu manifold such that ξ belongs to the (k, μ)′-nullity distribution and h′ 6= 0.

/pdf/on-ph-ricci-recurrent-almost-kenmotsu-manifolds-with-nullity-3iu6zo2tha.pdf

Krishanu Mandal

Papers

On ϕ-Ricci Recurrent Almost Kenmotsu Manifolds with Nullity Distributions