• Korean Journal of Mathematics
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• v.30 no.1
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• pp.61-66
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• 2022

A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.

• Korean Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.150-160
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• 1997

Existing non-manifold data structures which use the ordered topological representation method, are designed based on a "Model" which is the highest topological entity. Their non-manifold information is always included in edges and vertices even if they are in the manifold situation. Thus they require large storage spaces than manifold data structures. The proposed data structure reduces its storage space by removing unnecessary information stored in edges and vertices. Topological information is classified into manifold and non-manifold information. The main non-manifold information is radial cycles and disk cycles. The proposed data structure always stores manifold information. For the non-manifold situation, the edge stores radial cycles, and the vertex stores disk cycles. The storage space can be reduced in the later stage of CAD design when the ratio of non-manifold to manifold entities is small.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.401-408
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• 2009

The object of the present paper is to study certain curvature restriction on an LP-Sasakian manifold with a coefficient $\alpha$. Among others it is shown that if an LP-Sasakian manifold with a coefficient $\alpha$ is a manifold of constant curvature, then the manifold is the product manifold. Also it is proved that a 3-dimensional Ricci semisymmetric LP-Sasakian manifold with a constant coefficient $\alpha$ is a spaceform.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.3
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• pp.223-230
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• 2004

A method for measuring array manifold which is the array antenna response of incident signal is presented. Array manifold measurement procedure by the presented method is explained for UCA(Uniform Circular Array), and spatial spectrum of 300 ㎒ tone signal incident on UCA is estimated by MUSIC algorithm in which spatial spectrum peak is searched with measured array manifold. Spatial spectrum estimation using array manifold measured by the proposed method shows superior performance to calculated array manifold.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.481-485
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• 2009

Gabai's sutured manifold theory has produced many remarkable results in knot theory. Let M be the compact oriented 3-manifold and (M, ${\gamma}$) be sutured manifold. The aim of this note is to show that there exist a sutured manifold decomposition and a surface of M which defines a sutured manifold decomposition.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1306
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• 2020

An almost contact metric manifold is called a quasi contact metric manifold if the corresponding almost Hermitian cone is a quasi Kähler manifold, which was introduced by Y. Tashiro [9] as a contact O*-manifold. In this paper, we show that a quasi contact metric manifold with Killing characteristic vector field is a K-contact manifold. This provides an extension of the definition of K-contact manifold.

• Korean Journal of Mathematics
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• v.31 no.2
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• pp.139-144
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• 2023

In this paper, we show that a recurrent manifold with harmonic curvature tensor is locally symmetric and that an Einstein and conformally recurrent manifold is locally symmetric. As a consequence, Einstein and recurrent manifolds must be locally symmetric. On the other hand, we have obtained some results for a (conformally) recurrent manifold with parallel vector field and also investigated some results for a (conformally) recurrent manifold with concircular vector field.

• 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.45 no.2
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• pp.325-339
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• 2023

The object of the present work is to study a generalized W₃ recurrent manifold. We obtain a necessary and sufficient condition for the scalar curvature to be constant in such a manifold. Also, sufficient condition for generalized W₃ recurrent manifold to be special quasi-Einstein manifold are given. Ricci symmetric and decomposable generalized W₃ recurrent manifold are studied. Finally, the existence of such a manifold is ensured by a non-trivial example.