• Honam Mathematical Journal
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• v.38 no.1
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• pp.59-69
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• 2016

We classify conformally flat Kenmotsu 3-manifolds and classify conformally flat cosympletic 3-manifolds.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.411-424
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• 2002

We construct the canonical connection associated with a hypercontact structure. Moreover, we discuss the canonical connection associated with a sub-Riemannian 3-structure. As an application, we study the sub-symmetry property in terms of the canonical connection.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.81-99
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• 2006

We investigate a curvature-like tensor defined by (3.1) in Sasakian manifold of $dimension{\geq}$ 5, and show that this tensor satisfies some properties. Especially, we determine compact Sasakian manifolds with vanishing this tensor and improve some theorems concerning contact conformal curvature tensor and spectrum of Laplacian acting on $p(0{\leq}P{\leq}2)-forms$ on the manifold by using this tensor component.

• 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.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.417-424
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• 2017

In this paper, we study slant curves in a 3-dimensional almost f-Kenmotsu manifold with proper mean curvature vector field.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.863-881
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• 2014

Many differential geometric properties of a submanifold of a Kaehler manifold are conceived via canonical structure tensors T and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product if and only if T is parallel on the submanifold (c.f. [2]). Warped product submanifolds are generalized version of CR-product submanifolds. Therefore, it is natural to see how the non-triviality of the covariant derivatives of T and F gives rise to warped product submanifolds. In the present article, we have worked out characterizations in terms of T and F under which a contact CR- submanifold of a Kenmotsu manifold reduces to a warped product submanifold.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.179-191
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• 2022

We set our target to investigate Yamabe solitons, gradient Yamabe solitons and gradient Einstein solitons within the structure of 3-dimensional non-cosymplectic normal almost contact metric manifolds. Also, we provide a nontrivial example and validate a result of our paper.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.547-554
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• 2021

The object of the present paper is to characterize Sasakian 3-manifolds admitting a gradient Ricci-Yamabe soliton. It is shown that a Sasakian 3-manifold M with constant scalar curvature admitting a proper gradient Ricci-Yamabe soliton is Einstein and locally isometric to a unit sphere. Also, the potential vector field is an infinitesimal automorphism of the contact metric structure. In addition, if M is complete, then it is compact.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.541-549
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• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.181-189
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• 2000

Let (X, J) be a closed, connected almost complex four-manifold. Let $X_1$ be the complement of an open disc in X and let ${\varepsilon}_1$be the contact structure on the boundary ${\varepsilon}X_1$ which is compatible with a symplectic structure on $X_1$, Then we show that (X, J) is symplectic if and only if the contact structure ${\varepsilon}_1$ on ${\varepsilon}X_1$ is isomorphic to the standard contact structure on the 3-sphere $S^3$ and ${\varepsilon}X_1$is J-concave. Also we show that there is a contact structure ${\varepsilon}_0\ on\ S^2\times\ S^1$which is not strongly symplectically fillable but symplectically fillable, and that $(S^2{\times}S^1,\;{\varepsilon})$ has infinitely many non-diffeomorphic minimal fillings whose restrictions on$\S^2\times\ S^1$are ${\sigma}$ where ${\sigma}$ is the restriction of the standard symplectic structure on $S^2{\times}D^2$.