• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.951-962
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• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.333-340
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• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.625-638
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• 2016

In this paper, we introduce the notion of semi-slant lightlike submanifolds of indefinite Sasakian manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions $D_1$, $D_2$ and RadTM on semi-slant lightlike submanifolds of an indefinite Sasakian manifold have been obtained. We also obtain necessary and sufficient conditions for foliations determined by above distributions to be totally geodesic.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.441-460
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• 2016

We introduce the notions of h-v-semi-slant submersions and almost h-v-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations, investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. We find a condition for such submersions to be totally geodesic. We also obtain an inequality of a h-v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and h-v-semi-slant angle. Finally, we give examples of such maps.

• Communications of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.152-166
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• 2021

In this paper, we study the geometry of semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. The integrability conditions of distributions D1 ⊕ {V}, D2 ⊕ {V} and RadTM on semi-slant lightlike submanifolds of an indefinite Kenmotsu manifold are defined. Furthermore, we derive necessary and sufficient conditions for the above distributions to have totally geodesic foliations.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.699-715
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• 2022

We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension 2, and exhibit connections to various problems in dimension 3.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.599-620
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• 2023

In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.

• The Journal of the Petrological Society of Korea
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• v.14 no.2 s.40
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• pp.108-115
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• 2005

Gyeonggi metamorphic complex in the Gwangju area include banded biotite gneiss and quartzofeldspathic gneiss. Detailed structural analysis suggests that structural elements in the study area were formed by at least five phase of deformations. Penetrative compositional foliations(S1) formed in the banded gneiss during the first metamorphism and deformation (D1). After intrusion of plutonic rocks, the second deformation (D2) produced S2 foliations in the banded gneiss and quartzofeldspathic gneiss during the second metamorphism. D3 structures are represented by isoclinal folds (F3) whose axial surfaces are parallel to S3 foliations. The N-S oriented shortening (D4) was accommodated by closed upright F4 fold with about 100m of axial surface separation. F4 fold is refolded by regional F5 folding resulting in different orientation and fold style of F4 fold according to the position of F5 fold. The F4 fold with tight interlimb angle is subparallel to the axial surface (north-south) of F5 fold in the core of the F5 fold. In contrast the F4 fold trends northeast in the western limb and northwest in the eastern limb of F5 fold. The interlimb angle is larger in the limbs than that in the core of F5 fold. The trace of foliations is constrained by mainly F4 and F5 folds. Joint fanning around fold is developed in the limbs of F5 fold and bc joints are dominant in the hinge area of F5 fold. A strike-slip fault had developed in tile central part of the study area after F5 folding. The orientation of joint and foliation is rotated anticlockwise about $15^{\circ}$ by the landslide occurred during the Quaternary.

• Economic and Environmental Geology
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• v.48 no.6
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• pp.431-449
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• 2015

The study area is located in the western part of the Precambrian stock type of Sancheong anorthosite complex, the Jirisan province of the Yeongnam massif, in the southern part of the Korean Peninsula. We perform a detailed field geological investigation on the Sancheong anorthosite complex, and report the characteristics of lithofacies, occurrences, foliations, and research formation process and its mechanism of the Sancheong anorthosite complex. The Sancheong anorthosite complex is classified into massive and foliation types of Sancheong anorthosite (SA), Fe-Ti ore body (FTO), and mafic granulite (MG). Foliations are developed in the Sancheong anorthosite complex except the massif type of SA. The foliation type of SA, FTO, MG foliations are magmatic foliations which were formed in a not fully congealed state of SA from a result of the flow of FTO and MG melts and the kinematic interaction of SA blocks, and were continuously produced in the comagmatic differentiation. The Sancheong anorthosite complex is formed as the following sequence: the massive type of SA (a primary fractional crystallization of parental magmas under high pressure)${\rightarrow}$ the foliation type of SA [a secondary fractional crystallization of the plagioclase-rich crystal mushes (anorthositic magmas) primarily differentiated from parental magmas under low pressure]${\rightarrow}$the FTO (an injection by filter pressing of the residual mafic magmas in the last differentiation stage of anorthositic magmas into the not fully congealed SA)${\rightarrow}$the MG (a solidification of the finally residual mafic magmas). It indicates that the massive and foliation types of SA, the FTO, and the MG were not formed from the intrusion and differentiation of magmas which were different from each other in genesis and age but from the multiple fractionation and polybaric crystallization of the coeval and cogenetic magma.