• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.

• 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.49 no.5
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• pp.1101-1129
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• 2012

We study the geometry of the images of 1-dimensional homogeneous submersions for each of the model spaces X of the eight 3-dimensional geometries. In particular, We shall calculate the group of isometries and the curvatures of the base surfaces for each of the model spaces of 3-dimensional geometries, with respect to every closed subgroup of the isometries of X acting freely.

• Economic and Environmental Geology
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• v.24 no.1
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• pp.43-55
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• 1991

The Imgye area, in the NE Taebaegsan Region, consists of Precambrian granites and schist complex at the base and Paleozoic sedimentary rocks and amphibolite at cover. The granites in the area were previously thought to be Paleozoic in age, but recent geochronological data yields isotopic age ranging from $1837{\pm}82Ma$ to $2108{\pm}82Ma$ by Rb-Sr whole rock method. Therefore, basement-cover relations in the area should be reexamined. During the study, mylonite zone recognized along the contact boundary between Precambrian granites and Cambrian Jangsan Quartzite Formation. Mylonite zone has 150 - 250 m in width. Mylonitic rocks can divide into two groups; quartz mylonite derived from Jangsan Formation and mylonitic granites from Precambrian granites. Intensity of mylonitic foliation decreased toward the north. Amphibolite occurs as an intrusive sills within mylonite zone. Mineral fabrics and small scale shear zones are commonly seen in amphibolite. It indicates that intrusive age of amphibolite is synchronous to the formation of mylonite zone. Mylonite zone was reactivated as ductile thrust faults and forms the hinterland dipping imbricate zone during the Cretaceous Bulkuksa Orogeny. The near parallelism of mineral stretching lineation and long axis of strain ellipes indicates that the area is affected by a homogeneous pure shear flattening together with the variable components of simple shear.

• Economic and Environmental Geology
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• v.51 no.3
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• pp.213-222
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• 2018

Metasediment-hosted Pb-Zn mineralized zone has been found in Dyusembay of Kazakhstan. Its petrological properties, metal index, alteration index and redox-sensitivity are compared with those of SEDEX type deposit. Mineralization is developed along foliation of host rock (graphitic phyllite) and controlled by folds and faults; major ore minerals including pyrite, pyrrhotite, sphalerite, and galena are disseminated or interlayered with fine-grained quartz. The margin of the mineralized zone is metamorphosed accompanying sericite and chlorite. Hydrothermal brecciation and Pb-Zn mineralization formed in quartz-calcite stockworks are confirmed at the around of Maytyubin granitoid intrusions. The mineralization is classified into three types according to those of occurrence, paragenesis, chemical composition and isotopic characteristics. Type 1 whose fine-grained pyrite, pyrrhotite and sphalerite are formed in parallel yet discontinuous to well-developed foliations of the host rock; its geochemistry is similar to those of the earlier stage in SEDEX-type mineralization. In case of type 2, the ore minerals of which are concentrated being parallel to a foliation by regional metamorphism, and most of them associated with quartz and muscovite (${\pm}$ biotite) paragenetically. Type 3 is formed in the hydrothermal breccia zone whose ore minerals are controlled by foliation and breccia and developed in quartz ${\pm}$ calcite veins having a form such as stratification, stockwork or veinlets. Host rocks in the mineralized zone indicate homogeneous metamorphic grade and there is no specific alteration zonation. Also, all types (type 1, type 2, and type 3) represent similar REEs patterns, it can be interpreted that these are originated from a same source. Sulphides occurred in mineralized zone indicate a limited range of sulphur isotope values (type 2, ${\delta}^{34}S=-13.3{\sim}-11.7$‰; type 3, ${\delta}^{34}S=-13.9{\sim}-8.2$‰), and a result of geothermometry presents different temperature ranges: type 2($251{\pm}38^{\circ}C{\sim}277{\pm}40^{\circ}C$); type 3($360{\pm}2^{\circ}C$ to $537{\pm}29^{\circ}C$). It is estimated to be due to the effect of metamorphism and Maytyubin granitoid intrusions, respectively. In addition, ternary chart of thorium, scandium, and zircon for discrimination of tectonic setting and redox sensitivity using V/Mo values indicate that hydrothermal sediments put on reduction environment after precipitation, before being affected by metamorphism and intrusion activity. Geochemical data are plotted on a distal trend of SEDEX-type with discrimination plot using SEDEX index. As a result, petrological-geochemical properties demonstrate that Dyusembay Pb-Zn mineralized zone is comparable to distal-type of SEDEX deposit.

• The Journal of Engineering Geology
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• v.1 no.1
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• pp.54-67
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• 1991

In geological media with anisotropic properties, the strength anisotropy in intact rock is the most important issue in engineering aspects. Point-ioad(P/L) strength test designed to estimate the uniaxial compressive strength(${\sigma}_c$) can be used to evaluate the anisotropic strength characteristics of rocks. The relationship between ${\sigma}_c$ and P/L strength indices(I$_s$), obtained from the banded gneisses distributed in the Cheongyang area, varies depend mainly on the dip angle($\beta$) of foliation. The axial P/L strength indicies(I$_{sa}$) decreases with the increment of $\beta$, whereas diametral P/L strength indices(I$_{sa}$) increase with it. However, the ${\sigma}_c$ decreases with the increments of $\beta$ below about 40$^{\circ}$, but it increases with the increments of $\beta$ over about 40$^{\circ}$ in general. The correlation between ${\sigma}_c$ and I$_s$ suggests that ${\sigma}_c$ is related to the Isa withing low angle($\beta$<40$^{\circ}$) and the I$_{sd}$ within high angle ($\beta$>40$^{\circ}$), respectively. The ratios of I$_s$ to ${\sigma}_c$ are obtained as 11 to 14 in the the gneisses in the study area. The ratio of 24, which is generally adopted value, cannot always be truthworth to the gneisses in the study area. The ratio for the dykes, however, show a good correlation as 21 to 24.5 and, the value of 24 can be used for a homogeneous and isotropic materials such as dykes.