• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.893-900
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• 2023

In the present study, we consider some curvature properties of generalized B-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized B curvature tensor on Kenmostu manifold. Later we formulate generalized B pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized B ϕ-recurrent Kenmotsu manifold.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.261-272
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• 2018

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.951-964
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• 2016

The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.331-344
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• 2020

The objective of the present paper is to study certain curvature conditions in Kenmotsu manifolds with respect to the semi-symmetric non-metric connection. Finally, we construct an example of 5-dimensional Kenmotsu manifold with respect to the semi-symmetric non-metric connection to verify some results of the paper.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.257-266
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• 2010

We define a semi-symmetric non-metric connection in a nearly Kenmotsu manifold and we study semi-invariant submanifolds of a nearly Kenmotsu manifold endowed with a semi-symmetric non-metric connection. Moreover, we discuss the integrability of distributions on semi-invariant submanifolds of a nearly Kenmotsu manifold with a semi-symmetric non-metric connection.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.331-343
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• 2014

The object of the present paper is to study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold. In this paper, we study a semi-symmetric metric connection in an (${\varepsilon}$)-Kenmotsu manifold whose projective curvature tensor satisfies certain curvature conditions.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.175-185
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• 2022

The purpose of this paper is to study invariant submanifolds of a Lorentzian para Kenmotsu manifold. We obtain the necessary and sufficient conditions for an invariant submanifold of a Lorentzian para Kenmotsu manifold to be totally geodesic. Finally, a non-trivial example is built in order to verify our main 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.

• 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.42 no.3
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• pp.435-445
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• 2005

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.