• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.795-808
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• 2004

In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2119-2139
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• 2017

Here, certain Ricci flow for Finsler n-manifolds is considered and deformation of Cartan hh-curvature, as well as Ricci tensor and scalar curvature, are derived for spaces of scalar flag curvature. As an application, it is shown that on a family of Finsler manifolds of constant flag curvature, the scalar curvature satisfies the so-called heat-type equation. Hence on a compact Finsler manifold of constant flag curvature of initial non-negative scalar curvature, the scalar curvature remains non-negative by Ricci flow and blows up in a short time.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.317-326
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• 2012

We consider $N(k)$-quasi Einstein manifolds satisfying the conditions $C({\xi},\;X).S=0$, $\tilde{C}({\xi},\;X).S=0$, $\bar{P}({\xi},\;X).C=0$, $P({\xi},\;X).\tilde{C}=0$ and $\bar{P}({\xi},\;X).\tilde{C}=0$ where $C$, $\tilde{C}$, $P$ and $\bar{P}$ denote the conformal curvature tensor, the quasi-conformal curvature tensor, the projective curvature tensor and the pseudo projective curvature tensor, respectively.

• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.863-879
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• 2019

In this paper we study the Myers' theorem for orientable Riemannian hypersurfaces under some restrictions on the mean curvature, the second-order mean curvature, or the divergence of the shape operator and give some estimates for the diameter of such hypersurfaces.

• Journal of Korean Medicine Rehabilitation
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• v.20 no.1
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• pp.133-139
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• 2010

Objectives : The purpose of this study was to compare about quantity of pain and fatigue according to cervical spine curvature of patient with neck pain. Methods : Cervical spine curvature was measured using the sagittal radiography of the cervical spine, neck pain was evaluated using the VAS and neck fatigue was evaluated using fatigue symptom checklist. Based on four line Cobb's method, 51 subjects were divided into hypolordosis group, normal group, hyperlordosis group. Window version SPSS 12K was used for statistical analysis about relation between pain and cervical spine curvature of each group, also about between fatigue and cervical spine curvature of each group. Results : 1. A significant difference was not found between pain and cervical curvature of each group. 2. A significant difference was not found between fatigue and cervical curvature of each group. Conclusions : There was no relation between pain and cervical curvature of each group, also fatigue and cervical curvature.

• Journal of Korean Medicine Rehabilitation
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• v.21 no.2
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• pp.239-252
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• 2011

Objectives : To investigate and compare the curvature of the cervical spine for the neck pain patients and asymptomatic participants. Methods : Clinical study was carried out for 64 neck pain patients in Conmaul oriental hospital and 56 asymptomatic volunteers. Cervical spine curvature was measured by 7 types of measuring methods. Results : Curvature angles of the cervical spine were significantly lower in the patients group(p<0.05). In segmental analysis of curvature, segmental curvature of C3-C4 were significantly lower in the patients group. There is no significant relationship among the classifications by the types of cervical spine curvature in the 2 groups. Conclusions : The results suggest that the cervical spines of neck pain patients are straightened and kyphotic and most of cervical curvature decrease are occurred at middle cervical spine.

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.211-214
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• 2000

In this paper, we propose a regular-texture image retrieval approach relating In curvature. Maximum curvature and minimum curvature are computed from the query and each regular-texture image in the database. Seven features are computed from curvature characterizing statistical properties of the corresponding image. Each regular-texture image in the database is then represented as the seven CM (curvature measurement)-features. Query comparison and matching can be done using the corresponding CM-features. Experimental results on Brodatz texture show that the proposed approach is effective.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.115-128
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• 2014

In this paper, we study the second approximate Matsumoto metric F = ${\alpha}+{\beta}+{\beta}^2/{\alpha}+{\beta}^3/{\alpha}^2$ on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.279-293
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• 2002

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.647-655
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• 2013

We obtain $C^{\infty}$-continuous paths of explicit Riemannian metrics $g_t$, $0{\leq}t$ < ${\varepsilon}$, whose scalar curvatures $s(g_t)$ decrease, where $g_0$ is a flat metric, i.e. a metric with vanishing curvature. Most of them can exist on tori of dimension ${\geq}3$. Some of them yield scalar curvature decrease on a ball in the Euclidean space.