• Kyungpook Mathematical Journal
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• v.34 no.2
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• pp.283-291
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• 1994

• Honam Mathematical Journal
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• v.41 no.4
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• pp.769-780
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• 2019

We introduce anti-invariant Riemannian submersions from almost paracontact Riemannian manifolds onto Riemannian manifolds. We give an example, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and check the harmonicity of such submersions.

• Kyungpook Mathematical Journal
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• v.63 no.4
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• pp.593-610
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• 2023

In this paper, we prove the generalized Chen's conjecture for (𝓕, 𝓕')-biharmonic maps, such maps are critical points of the transversal bienergy functional.

• Journal of the Korean earth science society
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• v.21 no.4
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• pp.437-448
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• 2000

The Middle Carboniferous Gabsan Formation is distributed in the Cheongrim area of southern Yeongwol and the Mt. Gachang area of Chungbuk Province. This study was carried out to investigate the lithological characters and geochemical composition of the limestones and to find out controlling structures of the limestones of the formation. The limestones of the Gabsan Formation are characterized by the light gray to light brown in color and fine and dense textures. The limestone grains are composed of crinoid fragments, small foraminfers, fusulinids, gastropods, ostracods, etc. Due to the recrystallization, some limestones consist of fine crystalline calcites. The chemical analysis of limestones of the formation was conducted to find out the contents of CaO, MgO, Al$_2$O$_3$, Fe$_2$O$_3$ and SiO$_2$. The content of CaO ranges from 49.78-60.63% and the content of MgO ranges from 0.74 to 4.63% The contents of Al$_2$O$_3$ and Fe$_2$O$_3$ are 0.02-0.55% and 0.02${\sim}$0.84% , respectively. The content of SiO$_2$ varies from 1.55 to 4.80%, but some samples contain more than 6.0%. The limestones of the formation can be grouped into two according to the CaO content: One is a group of which CaO content ranges from 49.78 to 56.26% and the other is a group of which CaO content varies from 59.36 to 60.38%. In the first group, the contents of Al$_2$O$_3$, Fe$_2$O$_3$ and SiO$_2$ range very irregularly according to the CaO content. In the second group, the values of MgO, Al$_2$O$_3$, Fe$_2$O$_3$ and SiO$_2$ are nearly same. Detailed structural analysis of mesoscopic structures and microstructures indicates the five phase of deformation in the study area. The first phase of deformation(D$_1$) is characterized by regional scale isoclinal folds, and bedding parallel S$_1$ axial plane foliation which is locally developed in the mudstone and sandstone. Based on the observations of microstructures, S$_1$ foliations appear to be developed by grain preferred orientation accompanying pressure-solution. During second phase of deformation, outcrop scale E-W trending folds with associated foliations and lineations are developed. Microstructural observations indicate that crenulation foliations were formed by pressure-solution, grain boundary sliding and grain rotation. NNW and SSE trending outcrop scale folds, axial plane foliations, crenulation foliations, crenulation lineations, intersection lineations are developed during the third phase of deformation. On the microscale F$_3$ fold, axial plane foliations which are formed by pressure solution are well developed. Fourth phase of deformation is characterized by map scale NNW trending folds. The pre-existing planar and linear structures are reoriented by F$_4$ folds. Fifth phase of deformation developed joints and faults. The distribution pattern of the limestones is mostly controlled by F$_1$ and F$_4$ folds.

• The Journal of the Petrological Society of Korea
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• v.23 no.2
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• pp.105-117
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• 2014

The Ogcheon and Joseon Supergroups are distributed in the Bonghwajae area, Jecheon-si, Chungcheongbuk-do, Korea which is located in the northeastern fore-end of the Ogcheon Metamorphic Zone. This paper researched the geological structures based on the geometric and kinematic characteristics and the forming sequence of the major multi-deformed rock and microstructures. Most of regional foliations are not the S0 bedding but the S0-1 composite foliations defined by the preferred orientation of stretching minerals, some are recognized as the S0-1-2 composite foliations by the preferred orientation of insoluble opaque minerals and cleavage lamella. The geological structures were formed at least by three phases of deformations i.e. NNE-SSW trending D1, E-W trending D2, N-S trending D3 compressions. The S0-1 composite foliation, which shows a similar zone-distribution trend of the constitution strata of the Ogcheon and Joseon Supergroups, trended WNW before D2 deformation, but it was reoriented into N-S which was parallel to the trend of S2 foliation by D2 deformation, and it was rearranged into NW, NE, N-S trends as it is now by D3 deformation. The structural characteristics of each deformation phase and the deformation history are very similar to those in the eastern domain of Busan area into which the Ogcheon and Joseon Supergroups in this area are extended as NNW trend. It is expected to be very valuable data in interpreting the tectonic evolution of the northeastern fore-end of the Ogcheon Metamorphic Zone.

• The Journal of the Petrological Society of Korea
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• v.24 no.3
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• pp.209-231
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• 2015

In granite quarry, stones are generally quarried along easily separating planes called as 'rock cleavage'. Because orientation and characteristics of the rock cleavage are directly involved with easy quarrying, it is the most important factor on selecting a direction of digging. Using AMS (anisotropy of magnetic susceptibility), we attempt to interpret rock fabrics in Geochang Granite Stone (JS, SD, AR, GD, BW, MD quarry) and discuss about determination of rock cleavages and correlation between the rock fabrics and cleavages. Based on mean susceptibility, thermo-susceptibility curves, and hysteresis parameters, Ti-poor MD and/or PSD magnetites are the main contributor to AMS of the granite stones. The systematic magnetic foliations with sub-vertical dip angle are developed in the whole granite quarries. In most of the granite quarries, the magnetic foliations are significantly consistent with grain plane. In the BW quarry, which has higher $P_J$ values than the others, the magnetic foliations coincide exceptionally with rift plane. These results suggest that rock cleavages in granite stone are related to rock fabrics meaning shape and spatial arrangement of crystals. Magnetic fabrics analysis using AMS method, therefore, can be a quantitative and effective tool for determination of rock cleavages in granite quarry.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1169-1186
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• 2005

We study the properties of the transversal Killing and twistor spinors for a Riemannian foliation with a transverse spin structure. And we investigate the relations between them. As an application, we give a new lower bound for the eigenvalues of the basic Dirac operator by using the transversal twistor operator.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.165-173
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• 2017

In this paper, we prove that the automorphism group of a quasi-homogeneous properly convex affine domain in ${\mathbb{R}_n}$ acts transitively on the set of all the extreme points of the domain. This set is equal to the set of all the asymptotic cone points coming from the asymptotic foliation of the domain and thus it is a homogeneous submanifold of ${\mathbb{R}_n}$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1273-1283
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• 2018

Let ($M,{\mathcal{F}}$) be a closed, oriented Riemannian manifold of a foliation ${\mathcal{F}}$ with a nonisometric transversal conformal field. Then ($M,{\mathcal{F}}$) is transversally isometric to the sphere under some transversal concircular curvature conditions.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.591-602
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• 2012

In present paper we establish conditions for the integrability of various distributions of GCR-lightlike submanifolds and obtain conditions for the distributions to define totally geodesic foliations in GCR-lightlike submanifolds.