• 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 ${\mathbb{R}_n}$.

• Economic and Environmental Geology
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• v.40 no.6
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• pp.771-784
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• 2007

This study shows the weathering characteristics of mica-schist affected by faulting and metamorphism through laboratory tests. Frozen-thaw test, which simulate the physical-chemical weathering processes in the laboratory, shows the important influence of foliation developed in mica-schist, resulting in $20{\sim}40%$ reduction of UCS according to weathering grade of rock. Slaking durability test was carried out for different weathering grade rock specimens and indicated that the specimens from fault area had a low durability index compared to other relatively fresh samples. XRD analysis allowed to estimate the dynamic evolution of mineral composition through wet-dry cycle in which the chlorite was the most important mineral leached out during slaking test. The creep test indicated that the main deformation produced along the foliation plane. The compacted clay minerals between discontinuity planes influence on the discontinuity shearing properties and result in a big difference between peak shear strength and residual strength. The results of laboratory tests on mica-schist show the possibility of a important deformation along the foliation plane or discontinuity.

• Economic and Environmental Geology
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• v.33 no.2
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• pp.147-163
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• 2000

The Buseok pluton in the Yeongju Batholith is a comagmatic plutonic rocks which haveconcentrically compositional zoning. The lithofacies of the Buseok pluton comprise hornblende biotite tonalite in the southern part of the pluton, porphyritic and equigranular biotite granodiorite in the northern part and biotite granite in the north-central part. The compositional variations change gradually with continuity both within and between the lithofacies. The concentrically zoned pattern is relatively mafic rocks composed of high-temperature mineral assemblages in margin of the southern part, passing inward and northward gradually to more felsic rock in core of the north-central part. Changes in the textures and microstructures, as well as in the mineral content, take place between rock types of the plutons. Darker colored, generally coarse-grained, well foliated tonalite pass inward to light colored, coarse-grained, poorly foliated granodiorite, and finally give way to lighter colored, medium-grained, nearly nonfoliated granite. The foliation are best developed in the marginal part of the tonalite. Here, the regional myolitic foliation in the tonalite is steep northward and parallels to its southeastern contact with the country rock, but the magmatic foliation from disc-shaped mafic microgranitoid enclaves is subvertical and parallels the contacts with the country rock. As the tonalite approaches biotite granite in composition, the foliation is indistinct. Modal and chemical data for the pluton show quantitative compositional variation from the margin of the southern part to the core of the north-central part. Quartz and K-feldspar increase toward the core of the pluton, whereas hornblende, biotite and color index decrease. /Abundances of $SiO_2$and $K_2O$$_2$O increase toward the core according to the variation in quartz and K-feldspar, whereas those of MnO, CaO, $TiO_2$, $Fe_2O_3$, MgO and $P_2O_5$ decrease corresponding to the variation in mafic and accessaries. The compositional zonation resulted from fractional crystallization involving downward settling of earlier crystals, accompanied by upward movement of melt and volatiles, and followed by accessary marginal accretion of crystalline material in the magma to the marginal part. Although a little crustal contamination by the wall rock is recognized from the isotope data, the contamination is not only dominated over but also appropriate for forming the compositional variation in the pluton.

• The Journal of the Petrological Society of Korea
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• v.28 no.1
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• pp.25-38
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• 2019

The Muju-Seolcheon area, which is known to be located in the boundary of Ogcheon Belt and Ryeongnam Massif (OB-RM), consists of age unknown or Precambrian metamorphic rocks (MRs) [banded biotite gneiss, metasedimentary rocks (black phyllite, mica schist, crystalline limestone, quartzite), granitic gneiss, hornblendite], Mesozoic sedimentary and igneous rocks. In this paper are researched the structural characteristics of each deformation phase from the geometric and kinematic features and the developing sequence of multi-deformed rock structures of the MRs, and is considered the boundary location of OB-RM with the previous geochemical, radiometric, structure geological data. The geological structure of this area is at least formed through four phases (Dn-1, Dn, Dn+1, Dn+2) of deformation. The Dn-1 is the deformation which took place before the formation of Sn regional foliation and formed Sn-1 foliation folded by Fn fold. The Dn is that which formed the Sn regional foliation. The predominant Sn foliation shows a NE direction which matches the zonal distribution of MRs. A-type or sheath folds, in which the Fn fold axis is parallel to the direction of stretching lineation, are often observed in the crystalline limestone. The Dn+1 deformation, which folded the Sn foliation, took place under compression of NNW~NS direction and formed Fn+1 fold of ENE~EW trend. The Sn foliation is mainly rearranged by Fn+1 folding, and the ${\pi}$-axis of Sn foliation, which is dispersed, shows the nearly same direction as the predominant Fn+1 fold axis. The Dn+2 deformation, which folded the Sn and Sn+1 foliations, took place under compression of E-W direction, and formed open folds of N-S trend. And the four phases of deformation are recognized in all domains of the OB-RM, and the structural characteristics and differences to divide these tectonic provinces can not be observed in this area. According to the previous geochemical and radiometric data, the formation or metamorphic ages of the MRs in and around this area were Middle~Late Paleproterozoic. It suggests that the crystalline limestone was at least deposited before Middle Paleproterozoic. This deposition age is different in the geologic age of Ogcheon Supergroup which was recently reported as Neoproterozoic~Late Paleozoic. Therefore, the division of OB-RM tectonic provinces in this area, which regards the metasedimentary rocks containing crystalline limestone as age unknown Ogcheon Group, is in need of reconsideration.

• Journal of the Korean Mathematical Society
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• v.27 no.2
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• pp.167-175
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• 1990

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.51-60
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• 1995

Let $(M,g_M,F)$ be a (p+q)-dimensional connected Riemannian manifold with a foliation $F$ of codimension q and a complete bundle-like metric $g_M$ with respect to $F$. Let $Ric_D$ be the transverse Ricci field of $F$ with respect to the transverse Riemannian connection D which is a torsion-free and $g_Q$-metrical connection on the normal bundle Q of $F$. We consider transverse confomal (or, projective) fields of $F$. It is clear that a tranverse Killing field s of $F$ preserves the transverse Ricci field of $F$, that is, $\Theta(s)Ric_D = 0$, where $\Theta(s)$ denotes the transverse Lie differentiation with respect to s.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.769-777
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• 2011

It was obtained in [5] generalized Lichnerowicz and Obata theorems for Riemannian foliations, which reduce to the results on Riemannian manifolds for the point foliations. Recently in [3], they studied a generalized Obata theorem for Riemannian foliations admitting transversal conformal fields. Each transversal conformal field is a ${\lambda}$-automorphism with ${\lambda}=1-{\frac{2}{q}}$ in the sense of [8]. In the present paper, we extend certain results established in [3] and study Riemannian foliations admitting ${\lambda}$-automorphisms with ${\lambda}{\geq}1-{\frac{2}{q}}$.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1299-1307
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• 2020

We show that the Liechti-Strenner's example for the closed nonorientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial of the action induced on the first cohomology nonpositive. We also show that the Liechti-Strenner's example of orientation-reversing homeomorphism for the closed orientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial p(x) of the action induced on the first cohomology nonpositive or all but the first coefficient of p(x)(x ± 1)², p(x)(x² ± 1), or p(x)(x² ± x + 1) nonpositive.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.385-391
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• 1994

In this report, given a Riemannian foliation F on a Riemannian manifold, we introduce the concept of F-Jacobi fields along normal geodesics to investigate geometric properties of the leaves of F.(omitted)

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.1-7
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• 1999

We investigated the weathering characteristics of On-Yang gneiss by means of geological survey and Ground Penetrating Radar(GPR). The results of geological survey and boring show the two sets of vertical joint and horizontal joint developed by foliation which is composed of salic and melanic layers. GPR section evidently shows foliation direction and differential weathering due to discontinuity and mineral composition of metamorphic rock. The GPR section for instantaneous phase attribute based on complex trace analysis evidently shows continuity and foliation direction of metamorphic rock. The strong reflection amplitude which is derived from the banded structure of weathered rock can be incorrectly interpreted as a reflection of bedrock. The depth of rock basement should be estimated from the overall exploration result such as boring, seismic method, and electrical resistivity method.