• 대한수학회보
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• 제44권1호
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• pp.109-116
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• 2007

We study an (n+1)($(n{\geq}3)$-dimensional contact CR-submanifold of (n-1) contact CR-dimension in a (2m+1)-unit sphere $S^{2m+1}$, and to determine such sub manifolds under conditions concerning the second fundamental form and the induced almost contact structure.

• 충청수학회지
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• 제27권1호
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• pp.29-34
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• 2014

Almost contact and almost complex structures in the tangent bundle have been studied by K. Yano and S. Ishihara[5] and others. In the present paper, we have studied Lorentzian almost r-para-contact structure in the tangent bundle. Some results related to Lie-derivative have been studied.

• 대한수학회지
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• 제55권1호
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• pp.161-174
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• 2018

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

• 대한수학회보
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• 제21권2호
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• pp.61-66
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• 1984

It is well-known that the most interesting non-integrable almost Hermitian manifold are the nearly Kaehlerian manifolds ([2] and [3]), and that there exists a complex but not a Kaehlerian structure on Riemannian product manifolds of two normal contact manifolds [4]. The purpose of the present paper is to study nearly Kaehlerian product manifolds of two almost contact metric manifolds and investigate the geometrical structures of these manifolds. Unless otherwise stated, we shall always assume that manifolds and quantities are differentiable of class $C^{\infty}$. In Paragraph 1, we give brief discussions of almost contact metric manifolds and their Riemannian product manifolds. In paragraph 2, we investigate the perfect conditions for Riemannian product manifolds of two almost contact metric manifolds to be nearly Kaehlerian and the non-existence of a nearly Kaehlerian product manifold of contact metric manifolds. Paragraph 3 will be devoted to a proof of the following; A conformally flat compact nearly Kaehlerian product manifold of two almost contact metric manifolds is isomatric to a Riemannian product manifold of a complex projective space and a flat Kaehlerian manifold..

• 호남수학학술지
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• 제44권1호
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• pp.62-77
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• 2022

This study presents an 𝛼-Sasakian structure on the product manifold M₁ × 𝛽(I), where M₁ is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

• 충청수학회지
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• 제30권4호
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• pp.387-396
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• 2017

Our aim is to study covariant derivative with respect to complete and vertical lifts of generalized almost r-contact structure in tangent bundle.

• 충청수학회지
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• 제31권4호
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• pp.421-427
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• 2018

The aim of this study is to investigate the prolongations of G-structures immersed in the generalized almost r-contact structure on a manifold M to its tangent bundle T(M) of order 2. Moreover, theorems on Hsu structure, integrability and (${F\limits^{\circ}},\;{{\xi}\limits^{\circ}}{{\omega}\limits^{\circ}}_p,\;a,\;{\epsilon}$)-structure have been established.

• 충청수학회지
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• 제19권4호
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• pp.417-426
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• 2006

In this paper, we are to construct a new fibred Riemannian space with almost complex structure from the lift of an almost contact structures of the base space and that of each fibre. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structure.

• 대한수학회논문집
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• 제26권1호
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• pp.125-133
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• 2011

A new kind of structure is introduced in an even dimensional differentiable Riemannian manifold and some basic properties of this structure is discussed. Also the existence of such structure is shown with an example.

• 대한수학회지
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• 제46권1호
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.