• 자원환경지질
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• 제48권6호
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• pp.431-449
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• 2015

연구지역은 영남육괴 지리산지구에 분포하는 선캠브리아기 암주상 산청 회장암복합체 (이하, 회장암체)의 서부에 위치한다. 본 논문은 산청 회장암체에 대한 노두별 상세한 야외지질조사를 통하여 산청 회장암체의 암상, 엽리, 산상의 특징을 조사하고, 산청 회장암체의 형성과정과 그 메커니즘을 연구하였다. 산청 회장암체는 괴상형과 엽상형 산청 회장암 (이하, SA), 철-티탄 광체 (이하, FTO), 고철질 백립암 (이하, MG)으로 구분된다. 괴상형 SA를 제외한 산청 회장암체에는 엽리가 발달한다. 엽상형 SA, FTO, MG의 엽리는 SA가 완전히 고결되지 않은 물리적 상태에서 FTO 및 MG 용융체의 유동과 SA 블록들 사이의 상호운동의 결과로 형성된 마그마 엽리이며, 이들은 동원 마그마의 분화작용을 통해 연속적으로 형성되었다. 산청 회장암체는 괴상형 SA (고압 하에서 모 마그마의 1차 분별정출작용)${\rightarrow}$ 엽상형 SA [저압 하에서 모 마그마로부터 1차적으로 분화된 사장석-풍부 결정-용융 혼합체 (회장암질 마그마)의 2차 분별정출작용]${\rightarrow}$ FTO (회장암질 마그마의 2차 분별정출작용의 최종 분화단계에 잔류된 고철질 마그마의 압착여과작용에 의해 완전히 고화되지 않은 SA로 주입)${\rightarrow}$ MG (최종 잔류된 고철질 마그마의 고화작용) 순으로 형성되었다. 이는 산청 회장암체를 구성하는 괴상형과 엽상형 SA, FTO, MG는 성인과 시대를 달리하는 서로 다른 마그마의 분화 및 관입 산물이 아니라 동일시대의 동일기원 마그마로서 다단계 분별정출작용과 다중압력 결정화작용을 통해 형성되었음을 의미한다.

• 대한수학회지
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• 제41권5호
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• pp.865-874
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• 2004

The present paper treats with a subfoliation of a CR-foliation F on an almost Hermitian manifold M. When M is locally conformal almost Kahler, it has three OR-foliations. We show that a CR-foliation F on such manifold M admits a canonical subfoliation D(1/ F) defined by its totally real subbundle. Furthermore, we investigate some cohomology classes for D(1/ F). Finally, we construct a new one from an old locally conformal almost K hler (in particular, an almost generalized Hopf) manifold.

• 한국산업정보학회논문지
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• 제7권3호
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• pp.89-94
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• 2002

본 논문은 주로 개 f-코심플렉틱 다양체를 다룬다. 이 개념은 개 코심플렉틱 다양체와 개 겐모츠 다양체를 포함한다. 개 코심플렉틱 다양체는 ［1］에서 도입된 이래 ［2］, ［3］, ［4］ 등 여러 학자들에 의해 연구되어져 왔으며 개 겐모츠 다양체는 ［5］에서 도입된 이래 ［6］, ［7］ 등에서 연구되어져 왔다. 본 논문에서는 개f-코심플렉틱 다양체의 접촉 초함수에 의해 정의되는 정규 엽층구조의 기하학적 성질을 연구한다. 본 논문의 목적은 ［8］, ［9］에서 얻은 성과를 확장하는 것이다.

• 대한수학회지
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• 제49권6호
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• pp.1229-1257
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• 2012

We study the relation between an R-Cartan structure ${\alpha}$ an an (I, J, K)-generalized Finsler structure ${\omega}$ on a 3-manifold ${\Sigma}$ showing the difficulty in finding a general transformation that maps ${\alpha}$ to ${\omega}$. In some particular cases, the mapping can be uniquely determined by geometrical conditions. Moreover, we are led in this way to a negative answer to our conjecture in [12].

• Korean Journal of Mathematics
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• 제28권2호
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• pp.257-273
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• 2020

We introduce and study quasi hemi-slant submanifolds of almost contact metric manifolds (especially, cosymplectic manifolds) and validate its existence by providing some non-trivial examples. Necessary and sufficient conditions for integrability of distributions, which are involved in the definition of quasi hemi-slant submanifolds of cosymplectic manifolds, are obtained. Also, we investigate the necessary and sufficient conditions for quasi hemi-slant submanifolds of cosymplectic manifolds to be totally geodesic and study the geometry of foliations determined by the distributions.

• 대한수학회지
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• 제45권3호
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• pp.859-870
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• 2008

In the present paper, we investigate the geometric structures of the Dirichlet manifold composed of the Dirichlet distribution. We show that the Dirichlet distribution is an exponential family distribution. We consider its dual structures and give its geometric metrics, and obtain the geometric structures of the lower dimension cases of the Dirichlet manifold. In particularly, the Beta distribution is a 2-dimensional Dirich-let distribution. Also, we construct an affine immersion of the Dirichlet manifold. At last, we give the e-flat hierarchical structures and the orthogonal foliations of the Dirichlet manifold. All these work will enrich the theoretical work of the Dirichlet distribution and will be great help for its further applications.

• 대한수학회보
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• 제46권5호
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• pp.931-940
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• 2009

Given a system of smooth 1-forms $\theta$ = ($\theta^1$,...,$\theta^s$) on a smooth manifold $M^m$, we give a necessary and sufficient condition for M to be foliated by integral manifolds of dimension n, n $\leq$ p := m - s, and construct an integrable supersystem ($\theta,\eta$) by finding additional 1-forms $\eta$ = ($\eta^1$,...,$\eta^{p-n}$). We also give a necessary and sufficient condition for M to be foliated by reduced submanifolds of dimension n, n $\geq$ p, and construct an integrable subsystem ($d\rho^1$,...,$d\rho^{m-n}$) by finding a system of first integrals $\rho=(\rho^1$,...,$\rho^{m-n})$. The special case n = p is the Frobenius theorem on involutivity.

• 대한수학회논문집
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• 제35권2호
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• pp.591-602
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• 2020

There is a well-known class of compact, complex, non-Kählerian manifolds constructed by Bosio, called the LVMB manifolds, which properly includes the Hopf manifold, the Calabi-Eckmann manifold, and the LVM manifolds. As in the case of LVM manifolds, these LVMB manifolds can admit a regular holomorphic foliation 𝓕. Moreover, later Meersseman showed that if an LVMB manifold is actually an LVM manifold, then the regular holomorphic foliation 𝓕 is actually transverse Kähler. The aim of this paper is to deal with a converse question and to give a simple and new proof of a well-known result of Cupit-Foutou and Zaffran. That is, we show that, when the holomorphic foliation 𝓕 on an LVMB manifold N is transverse Kähler with respect to a basic and transverse Kähler form and the leaf space N/𝓕 is an orbifold, N/𝓕 is projective, and thus N is actually an LVM manifold.

• 대한수학회논문집
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• 제32권3호
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• pp.725-743
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• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• 호남수학학술지
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• 제42권4호
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.