• Journal of applied mathematics & informatics
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• v.6 no.3
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• pp.921-928
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• 1999

K. Kenmotsu introduced and studied the so-called Kenmotsu manifold related to the warped product space. In this paper we charac-terize a Kenmotsu Manifold using the fibred Riemannian space.

• 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.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.637-645
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• 2014

We study 3-dimensional non-unimodular Lie groups with a left-invariant almost Kenmotsu structure.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.793-805
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• 2017

In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying ${\nabla}_{\xi}h=0$, $h{\neq}0$, is ${\eta}$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^2(-4){\times}\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.655-665
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• 2021

In the present paper, we study the geometric properties of the invariant submanifold of an almost Kenmotsu structure whose Riemannian curvature tensor has (𝜅, 𝜇, 𝜈)-nullity distribution. In this connection, the necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu (𝜅, 𝜇, 𝜈)-space to be totally geodesic under the behavior of functions 𝜅, 𝜇, and 𝜈.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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• pp.1303-1336
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• 2023

In this paper, we study the 𝜂-parallelism of the Ricci operator of almost Kenmotsu 3-manifolds. First, we prove that an almost Kenmotsu 3-manifold M satisfying ∇_𝜉h = -2𝛼h𝜑 for some constant 𝛼 has dominantly 𝜂-parallel Ricci operator if and only if it is locally symmetric. Next, we show that if M is an H-almost Kenmotsu 3-manifold satisfying ∇_𝜉h = -2𝛼h𝜑 for a constant 𝛼, then M is a Kenmotsu 3-manifold or it is locally isomorphic to certain non-unimodular Lie group equipped with a left invariant almost Kenmotsu structure. The dominantly 𝜂-parallelism of the Ricci operator is equivalent to the local symmetry on homogeneous almost Kenmotsu 3-manifolds.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.341-358
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• 2023

Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with 𝛽-Kenmotsu structure. It is proven that a (2n + 1)-dimensional generalized Sasakian-space-form with 𝛽-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with 𝛽-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either ψ∖T^k × M^2n+1-k or gradient 𝜂-Yamabe soliton.

• 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.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.1-10
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• 2014

In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.321-331
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• 2019

The present paper deals with a study of infinitesimal CL-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to CL-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on 3-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.