• Korean Journal of Mathematics
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• 제29권4호
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• pp.705-714
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• 2021

In the present paper, we study 𝜂-Ricci solitons on para-Kenmotsu manifolds with Codazzi type of the Ricci tensor. We study 𝜂-Ricci solitons on para-Kenmotsu manifolds with cyclic parallel Ricci tensor. We also study 𝜂-Ricci solitons on 𝜑-conformally semi-symmetric, 𝜑-Ricci symmetric and conformally Ricci semi-symmetric para-Kenmotsu manifolds. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits 𝜂-Ricci solitons.

• 대한수학회논문집
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• 제28권2호
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• pp.353-360
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• 2013

We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

• 대한수학회논문집
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• 제39권1호
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• pp.175-186
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• 2024

In this paper, we study para-Kenmotsu manifolds admitting generalized η-Ricci solitons associated to the Zamkovoy connection. We provide an example of generalized η-Ricci soliton on a para-Kenmotsu manifold to prove our results.

• 대한수학회논문집
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• 제33권1호
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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.

• 호남수학학술지
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• 제41권4호
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• pp.669-682
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• 2019

The objective of this paper is to introduce and study Einstein-like para-Kenmotsu manifolds. For a para-Kenmotsu manifold to be Einstein-like, a necessary and sufficient condition in terms of its curvature tensor is obtained. We also obtain the scalar curvature of an Einstein-like para-Kenmotsu manifold. A necessary and sufficient condition for an almost para-contact metric hypersurface of a locally product Riemannian manifold to be para-Kenmotsu is derived and it is shown that the para-Kenmotsu hypersurface of a locally product Riemannian manifold of almost constant curvature is always Einstein.

• 호남수학학술지
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• 제43권4호
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• pp.613-626
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• 2021

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

• Korean Journal of Mathematics
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• 제29권2호
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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.

• 대한수학회지
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• 제39권6호
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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.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.475-490
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• 2022

The main purpose of the present paper is to introduce a brief analysis on some properties of quasi hemi-slant submanifolds of Kenmotsu manifolds. After discussing the introduction and some preliminaries about the Kenmotsu manifold, we worked out some important results in the direction of integrability of the distributions of quasi hemi-slant submanifolds of Kenmotsu manifolds. Afterward, we investigate the conditions for quasi hemi-slant submanifolds of a Kenmotsu manifold to be totally geodesic and later we provide some non-trivial examples to validate the existence of such submanifolds.

• 대한수학회보
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• 제54권1호
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• pp.85-97
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• 2017

We classify Kenmotsu 3-manifolds and cosymplectic 3-manifolds with ${\eta}-parallel$ Ricci operator.