• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.237-249
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• 2002

We study nondegenerate immersions of Riemannian manifolds of constant sectional curvatures into Lorentzian manifolds of the same constant sectional curvatures with flat normal bundles. We also give a method to produce such immersions using the so-called Grassmannian system. .

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1221-1244
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• 2020

In this paper we consider L_K-conjecture introduced in [5, 6] for hypersurface Mⁿ in space form Rⁿ⁺¹(c) with three principal curvatures. When c = 0, -1, we show that every L₁-biharmonic hypersurface with three principal curvatures and H₁ is constant, has H₂ = 0 and at least one of the multiplicities of principal curvatures is one, where H₁ and H₂ are first and second mean curvature of M and we show that there is not L₂-biharmonic hypersurface with three disjoint principal curvatures and, H₁ and H₂ is constant. For c = 1, by considering having three principal curvatures, we classify L₁-biharmonic hypersurfaces with multiplicities greater than one, H₁ is constant and H₂ = 0, proper L₁-biharmonic hypersurfaces which H₁ is constant, and L₂-biharmonic hypersurfaces which H₁ and H₂ is constant.

• The Journal of Churna Manual Medicine for Spine and Nerves
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• v.2 no.2
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• pp.1-16
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• 2007

Objectives : The purpose of this study was to identify spinal curvatures, plantar pressure and foot angles in a walking. Methods : 19 outpatients under 19 years old were included. Plantar pressure and foot angle in a walking were measured by using Gaitview AFA-50. Spinal curvatures were measured by using radiograph. Results : The cervical lordotic angle is significantly difference with left and right plantar pressure(p=0.027). The thoracic kyphotic angle is significantly difference with left and right plantar pressure(p=0.026). Cobb's angle is significantly difference with left and right plantar pressure(p=0.027). The other plantar pressure were no difference from spinal curvatures and foot angle in a walking. Conclusion : There were no correlation between plantar pressure, spinal curvatures and foot angle. We consider that needed more additional study.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.285-293
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• 2012

In this paper, we investigate the hypersurface M in a unit sphere with constant k-th mean curvature and two distinct principal curvatures, and characterize such a hypersurface.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.29-48
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• 2008

We deal with the classification problem of real hypersurfaces in a complex hyperbolic space. In order to classify real hypersurfaces in a complex hyperbolic space we characterize a real hypersurface M in $H_n(\mathbb{C})$ whose structure vector field is not principal. We also construct extrinsically homogeneous real hypersurfaces with four distinct curvatures and their structure vector fields are not principal.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.41-61
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• 2008

We study Lorentzian surfaces with the constant Gaussian curvatures or the constant mean curvatures in the 3-dimensional Lorentzian space and their transformations. Such surfaces are associated to the Lorentzian Grassmannian systems and some transformations on such surfaces are given by dressing actions on those systems.

• Kyungpook Mathematical Journal
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• v.62 no.2
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• pp.323-331
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• 2022

In this paper, we present a formula for pseudohermitian curvatures on bounded strictly pseudoconvex domains in ℂ² with respect to the coefficients of adapted frames given by Graham and Lee in [3] and their structure equations. As an application, we will show that the pseudohermitian curvatures on strictly plurisubharmonic exhaustions of Thullen domains diverges when the points converge to a weakly pseudoconvex boundary point of the domain.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1215-1231
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• 2023

The present article contains the study of D-homothetically deformed f-Kenmotsu manifolds. Some fundamental results on the deformed spaces have been deduced. Some basic properties of the Riemannian metric as an inner product on both the original and deformed spaces have been established. Finally, applying the obtained results, soliton functions, Ricci curvatures and scalar curvatures of almost Riemann solitons with several kinds of potential vector fields on the deformed spaces have been characterized.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.67-74
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• 2024

Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃³ in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.