• Korean Journal of Mathematics
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• v.29 no.2
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• pp.333-344
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• 2021

In the present paper, we study three-dimensional f-Kenmotsu manifolds admitting the Schouten-Van Kampen connection. We study the concircular curvature tensor of a three-dimensional f-Kenmotsu manifold with respect to the Schouten-Van Kampen connection. Finally, we have cited an example of a three-dimensional f-Kenmotsu manifold admitting Schouten-Van Kampen connection which verify our results.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.1-10
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• 2022

In the present paper, we have studied conformal Ricci solitons on f-Kenmotsu manifolds of dimension three. Also we have studied 𝜙-Ricci symmetry, 𝜂-parallel Ricci tensor, cyclic parallel Ricci tensor and second order parallel tensor in f-Kenmotsu manifolds of dimension three admitting conformal Ricci solitons. Finally, we give an example.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1215-1231
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• 2023

The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.309-318
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• 2017

The object of the present paper is to study almost Ricci solitons and gradient almost Ricci solitons in 3-dimensional f-Kenmotsu manifolds.

• The Pure and Applied Mathematics
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• v.27 no.2
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• pp.83-96
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• 2020

In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional f-Kenmotsu manifolds. We also study 1-type curves in a three dimensional f-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional f-Kenmotsu manifold with the curvature κ and the torsion τ, κ² + τ² = -(f² + f'). Also we prove that if a 1-type non-geodesic biharmonic curve γ is helix, then λ = -(f² + f').

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.953-961
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• 2002

Generalized Ricci-recurrent trans-Sasakian manifolds are studied. Among others, it is proved that a generalized Ricci-recurrent cosymplectic manifold is always recurrent Generalized Ricci-recurrent trans-Sasakian manifolds of dimension $\geq$ 5 are locally classified. It is also proved that if M is one of Sasakian, $\alpha$-Sasakian, Kenmotsu or $\beta$-Kenmotsu manifolds, which is gener-alized Ricci-recurrent with cyclic Ricci tensor and non-zero A (ξ) everywhere; then M is an Einstein manifold.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.547-560
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• 2023

For a pseudo-slant submanifold of a Kenmotsu manifold, we have worked out conditions in terms its canonical structure tensors, T and F, and its shape operator so that it reduces to a warped product submanifold.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.717-732
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• 2023

The goal of this paper is to analyze the generalized m-quasi-Einstein structure in the context of almost Kenmotsu manifolds. Firstly we showed that a complete Kenmotsu manifold admitting a generalized m-quasi-Einstein structure (g, f, m, λ) is locally isometric to a hyperbolic space ℍ²ⁿ⁺¹(-1) or a warped product ${\tilde{M}}{\times}{_{\gamma}{\mathbb{R}}$ under certain conditions. Next, we proved that a (κ, µ)'-almost Kenmotsu manifold with h' ≠ 0 admitting a closed generalized m-quasi-Einstein metric is locally isometric to some warped product spaces. Finally, a generalized m-quasi-Einstein metric (g, f, m, λ) in almost Kenmotsu 3-H-manifold is considered and proved that either it is locally isometric to the hyperbolic space ℍ³(-1) or the Riemannian product ℍ²(-4) × ℝ.

• Journal of Korea Society of Industrial Information Systems
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• v.7 no.3
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• pp.89-94
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• 2002

The present paper mainly treats with almost f-cosymplectic manifolds. This notion contains almost cosymplectic and almost Kenmotsu manifolds. Almost cosymplectic manifolds introduced in ［1］ have been studied by many schalors, say ［2］, ［3］, ［4］, and almost Kenmotsu manifolds introduced in ［5］ have been studied in ［6］, ［7］. The present paper studies some geometrical and topological properties of the canonical foliation defined by the contact distribution of an almost f-cosymplectic manifold. The purpose of the present paper is to extend the results obtained in ［8］, ［9］.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.417-424
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• 2017

In this paper, we study slant curves in a 3-dimensional almost f-Kenmotsu manifold with proper mean curvature vector field.