• 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.

• Journal of the Korean Mathematical Society
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• v.11 no.2
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• pp.143-152
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• 1974

• Kyungpook Mathematical Journal
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• v.14 no.2
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• pp.195-201
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• 1974

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.180-185
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• 2003

In order to enhance dexterity in execution of robot tasks, a redundant number of degrees-of-freedom (DOF) is adopted for design of robotic mechanisms like robot arms and multi-fingered robot hands. Associated with such redundancy in the number of DOFs relative to the number of physical variables necessary and sufficient for description of a given task, an extra performance index is introduced for controlling such a redundant robot in order to avoid arising of an ill-posed problem of inverse kinematics from the task space to the joint space. This paper shows that such an ill-posedness of DOF redundancy can be resolved in a natural way by using a novel concept named “stability on a manifold”. To show this, two illustrative robot tasks 1) robotic handwriting and 2) control of an object posture via rolling contact by a multi-DOF finger are analyzed in details.

• Honam Mathematical Journal
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• v.41 no.4
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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.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.441-447
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• 2002

We show that the conharmonical1y flat K-contact find cosymplectic manifolds are local1y Euclidean. Evidently non locally Euclidean conharmonically flat Sasakian manifold does not exist. Moreover we see that conharmonically flat Kenmotsu manifold does not exist and conharmonically flat fibred quasi quasi Sasakian space is locally Euclidean if and only if the scalar curvature of each fibre vanishes identically.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.401-409
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• 1994

One of typical submanifolds of a Sasakian manifold is the so-called generic submanifolds which are defined as follows: Let M be a submanifold of a Sasakian manifold M with almost contact metric structure (ø, G, ξ) such that M is tangent to the structure vector ξ. If each normal space is mapped into the tangent space under the action of ø, M is called a generic submanifold of M [2], [8].(omitted)

• 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 $S^2{\times}D^2$.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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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.