• Honam Mathematical Journal
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• v.43 no.1
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• pp.35-46
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• 2021

The purpose of this paper is to study invariant pseudoparallel, Ricci generalized pseudoparallel and 2-Ricci generalized pseudoparallel submanifold of a para-Kenmotsu manifold and I obtained some equivalent conditions of invariant submanifolds of para-Kenmotsu manifolds under some conditions which the submanifolds are totally geodesic. Finally, a non-trivial example of invariant submanifold of paracontact metric manifold is constructed in order to illustrate our results.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.152-166
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• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.781-790
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• 2021

The goal of this paper is to characterize a class of almost Kenmotsu manifolds admitting *-conformal Ricci solitons. It is shown that if a (2n + 1)-dimensional (k, µ)'-almost Kenmotsu manifold M admits *-conformal Ricci soliton, then the manifold M is *-Ricci flat and locally isometric to ℍⁿ⁺¹(-4) × ℝⁿ. The result is also verified by an example.

• 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.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.97-104
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• 2023

In the present paper, we characterize, for a class of almost Kenmotsu manifolds, those that admit quasi Yamabe solitons. We show that if a (k, 𝜇)'-almost Kenmotsu manifold admits a quasi Yamabe soliton (g, V, 𝜆, 𝛼) where V is pointwise collinear with 𝜉, then (1) V is a constant multiple of 𝜉, (2) V is a strict infinitesimal contact transformation, and (3) (£_Vh')X = 0 holds for any vector field X. We present an illustrative example to support the result.

• 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.64 no.2
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• pp.261-270
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• 2024

In this paper, we consider generalized 𝜂-Ricci solitons associated to the general connection on Kenmotsu manifolds. We confirm the existence of such solitons by constructing a non-trivial example, and we obtain some properties of Kenmotsu manifolds that admit the generalized 𝜂-Ricci solitons associated with the general connection.

• East Asian mathematical journal
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• v.17 no.1
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• pp.103-114
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• 2001

When the target manifold is certain Kenmotsu manifolds, we characterize invariant immersions, tangential anti-invariant immersions and normal anti-invariant immersions by the spectra of the Jacobi operator.

• 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.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.707-722
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• 2014

In this paper, we study the forms of the curvatures of lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: M is locally symmetric or M is semi-symmetric.