• Title, Summary, Keyword: Curvature

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Relationship Between Curvature Angle and BMI According to Wearing a Scoliosis Brace (척추측만증보조기 착용에 따른 만곡각도와 체질량지수의 관계)

  • Lee, Gwangho
    • Journal of The Korean Society of Integrative Medicine
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    • v.7 no.3
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    • pp.149-157
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    • 2019
  • Purpose : This study aims to check the relationship between the size of curvature in scoliosis patients and the reduction rate of curvature after wearing a brace and the relationships of the size of curvature and correction angle with Body Mass Index (BMI). Methods : With 30 adolescent girls who had never worn a brace, their Cobb angle and BMI were measured before manufacturing braces, and their corrected Cobb angle was measured after wearing the manufactured scoliosis braces. Results : The size of the major curvature before wearing the brace and the reduction rate of the curvature after putting it on had a negative correlation in both the major curvature (r=-.465, p<.01) and the minor curvature (r=-.516, p<.01). The size of the minor curvature and the reduction rate of the minor curvature before and after putting it on also had a negative correlation (r=-.429, p<.05). As for the relationship between the size of curvature and BMI, they had a negative correlation in both the major curvature (r=-.141) and the minor curvature (r=-.123), and as for the relationship between the reduction rate of curvature and BMI after wearing the brace, they had a positive correlation in both the major curvature (r=.251) and the minor curvature (r=.136); however, it was not statistically significant (p>.05). Conclusion : In conclusion, the larger the size of curvature, the lower the reduction rate of curvature after wearing the brace became. The larger the size of curvature, the lower the BMI became. The higher the BMI, the higher the correction ratio of the brace became. Therefore, it is judged that it is necessary to provide early treatment and manage body composition before scoliosis progresses.

SOME INEQUALITIES ON TOTALLY REAL SUBMANIFOLDS IN LOCALLY CONFORMAL KAEHLER SPACE FORMS

  • Alfonso, Carriazo;Kim, Young-Ho;Yoon, Dae-Won
    • 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.

Curvature Properties of 𝜂-Ricci Solitons on Para-Kenmotsu Manifolds

  • Singh, Abhishek;Kishor, Shyam
    • Kyungpook Mathematical Journal
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    • v.59 no.1
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    • pp.149-161
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    • 2019
  • In the present paper, we study curvature properties of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds. We obtain some results of ${\eta}$-Ricci solitons on para-Kenmotsu manifolds satisfying $R({\xi},X).C=0$, $R({\xi},X).{\tilde{M}}=0$, $R({\xi},X).P=0$, $R({\xi},X).{\tilde{C}}=0$ and $R({\xi},X).H=0$, where $C,\;{\tilde{M}},\;P,\;{\tilde{C}}$ and H are a quasi-conformal curvature tensor, a M-projective curvature tensor, a pseudo-projective curvature tensor, and a concircular curvature tensor and conharmonic curvature tensor, respectively.

DISCRETE CURVATURE BASED ON AREA

  • Park, Kyeong-Su
    • Honam Mathematical Journal
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    • v.32 no.1
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    • pp.53-60
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    • 2010
  • The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.

VISUAL CURVATURE FOR SPACE CURVES

  • JEON, MYUNGJIN
    • Honam Mathematical Journal
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    • v.37 no.4
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    • pp.487-504
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    • 2015
  • For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.

On Quasi-Conformally Recurrent Manifolds with Harmonic Quasi-Conformal Curvature Tensor

  • Shaikh, Absos Ali;Roy, Indranil
    • Kyungpook Mathematical Journal
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    • v.51 no.1
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    • pp.109-124
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    • 2011
  • The main objective of the paper is to provide a full classification of quasi-conformally recurrent Riemannian manifolds with harmonic quasi-conformal curvature tensor. Among others it is shown that a quasi-conformally recurrent manifold with harmonic quasi-conformal curvature tensor is any one of the following: (i) quasi-conformally symmetric, (ii) conformally flat, (iii) manifold of constant curvature, (iv) vanishing scalar curvature, (v) Ricci recurrent.

A NEW 3-PARAMETER CURVATURE CONDITION PRESERVED BY RICCI FLOW

  • Gao, Xiang
    • Journal of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.829-845
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    • 2013
  • In this paper, we firstly establish a family of curvature invariant conditions lying between the well-known 2-nonnegative curvature operator and nonnegative curvature operator along the Ricci flow. These conditions are defined by a set of inequalities involving the first four eigenvalues of the curvature operator, which are named as 3-parameter ${\lambda}$-nonnegative curvature conditions. Then a related rigidity property of manifolds with 3-parameter ${\lambda}$-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the 3-parameter ${\lambda}$-nonnegativity along Ricci flow.

ON GENERALIZED QUASI-CONFORMAL N(k, μ)-MANIFOLDS

  • Baishya, Kanak Kanti;Chowdhury, Partha Roy
    • Communications of the Korean Mathematical Society
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    • v.31 no.1
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    • pp.163-176
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    • 2016
  • The object of the present paper is to introduce a new curvature tensor, named generalized quasi-conformal curvature tensor which bridges conformal curvature tensor, concircular curvature tensor, projective curvature tensor and conharmonic curvature tensor. Flatness and symmetric properties of generalized quasi-conformal curvature tensor are studied in the frame of (k, ${\mu}$)-contact metric manifolds.

Effect of Curvature on Deformation caused by Thermal Plate Forming (열간가공의 변형에 미치는 곡률의 영향에 관한 연구)

  • Lee, Joo-Sung
    • Journal of Ocean Engineering and Technology
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    • v.25 no.2
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    • pp.67-72
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    • 2011
  • This study had the goal of investigating the effect of the curvature along the heating line on the transverse angular distortion of plates having an initial curvature from line heating. A thermo-elasto-plastic analysis was carried out using 54 models with various radii of curvature, plate thicknesses, and heating speeds. The results show the effect of the curvature along the heating line on the angular distortion in relation to changes in the magnitudes of the curvature, heating speed, and plate thickness. The present numerical results show that the time history of the angular distortion after cooling and reaching the final deformed shape for a plate having an initial curvature is quite different from that of a flat plate. This emphasized the importance of considering the curvature effect on the transverse angular distortion. From the viewpoint of the curvature effect on the deformation, it has been seen that the curvature does not affect the transverse shrinkage. In this study the predicting formula for the transverse angular distortion was derived through a regression analysis. It showed that as the curvature increased, the angular distortion was reduced because of the higher bending rigidity at the same heat input parameter, and the peak points moved toward the origin as the curvature increased.