• Journal of the Chungcheong Mathematical Society
• /
• v.34 no.1
• /
• pp.37-53
• /
• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.6
• /
• pp.1367-1382
• /
• 2020

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.547-557
• /
• 1998

In this paper, we study submanifolds in the Euclidean space with parallel normal mean curvature vectorand special quadric representation. Especially we give a complete classification result relative to surfaces satisfying these conditions.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.5
• /
• pp.1341-1353
• /
• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• Journal of the Korean Mathematical Society
• /
• v.39 no.2
• /
• pp.253-275
• /
• 2002

The purpose of this paper is to study complete complex submanifolds of a locally symmetric Kaehler manifold with non-positive totally real normal bisectional curvature and k-pinched totally real tangent bisectional curvature.

• Communications of the Korean Mathematical Society
• /
• v.24 no.2
• /
• pp.265-275
• /
• 2009

The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.

• Korean Journal of Applied Biomechanics
• /
• v.30 no.1
• /
• pp.93-101
• /
• 2020

Objective: The purpose of this study was to differences of foot plantar pressure balance and lung capacity according to cervical posture in adults. Method: The subjects consisted of 33 adults in their 20s and 50s who use M centers in B-gu and H-gu, B-City, and they measured foot plantar pressure balance and lung capacity according to cervical posture (cervical normal curvature posture, cervical flexural posture) in adults. Results: In this study, the difference of foot plantar pressure balance according to cervical posture were analyzed. In the difference between left and right foot pressure balance. It was 1.50% increased in the cervical flexural posture than in the cervical normal curvature posture, and a statistically significant difference was observed. In the difference between the anterior and posterior foot pressure balance. It was 4.28% increased in the cervical flexural posture than in the cervical normal curvature posture, and a statistically significant difference was observed. The difference of lung capacity according to cervical posture were analyzed. In the PEF, It was 58.63 l/min decreased in the cervical flexural posture than in the cervical normal curvature posture, and a statistically significant difference was observed. In the FEV1, It was 0.15 ℓ decreased in the cervical flexural posture than in the cervical normal curvature posture, and a statistically significant difference was observed. Conclusion: The results of this study suggest that had a positive effect on differences of foot plantar pressure balance and lung capacity at cervical normal curvature posture in adults. In future research, itis believed that research on the elderly who have collapsed the normal curvature posture due to aging, as well as teenagers whose normal curvature posture due to the use of smartphones, will contribute to the balance of foot pressure and improvement of the right cervical habits. In future studies, it is also believed that it will be necessary to measure lung capacity after performing exercise according to the cervical posture, thereby providing sufficient oxygen during exercise to enhance the persistence and efficiency of the movement.

• The Journal of Korean Academy of Prosthodontics
• /
• v.29 no.3
• /
• pp.181-196
• /
• 1991

The Purpose of this study was to evaluate the marginal fit of ceramo-metal crown according to the different ceramo-metal alloy types and the curvature of labio-cervical margin. Degudent $G^{(R)}$ as precious and $Verabond^{(R)}$ as non-precious ceramo-metal alloy were used. The abutment was preparaed with two different curvature types : a normal curvature type and a pronounced curvature type. 20 crowns were farbricated using four different combinations and their marginal fits were measured at 3 consecutive stages (before degassing, after degassing, after glazing) using microscope under 200 magnification. The results were as follows: 1 . Marginal fitness before degassing. The groups of precious ceramo-metal exhibited better marginal fit than the groups of non-precious ceramo-metal with significant difference(P<0.05) . In the same ceramo-metal groups, the normal curvature group exhibited better marginal fit than the pronounced curvature group but without significant difference(P>0.05). 2. Marginal fitness after degassing. By degassing, the group of pronounced curvature and non-precious ceramo-metal was deformed the most, and the degree of margin fitness of each group was the same as before degassing. 3. Marginal fitness after glazing The group of normal curvature and precious ceramo-metal exhibited better marginal fit than the group of pronounced curvature and non-precious ceramo-metal with significant difference(P>0.05), and the degree of margin fitness of each group was the same as before degassing.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.2
• /
• pp.211-218
• /
• 2014

In 3-dimensional Euclidean space, the geometric figures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry. In this paper, we define parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curvature of the surface with curvature and torsion of the given curve. In particular, we find some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.

• Computers and Concrete
• /
• v.2 no.4
• /
• pp.309-324
• /
• 2005

The moment-curvature relationship of reinforced concrete beams made of normal- and high-strength concrete experiencing complex load history is studied using a numerical method that employs the actual stress-strain curves of the constitutive materials and takes into account the stress-path dependence of the concrete and steel reinforcement. The load history considered includes loading, unloading and reloading. From the results obtained, it is found that the complete moment-curvature relationship, which is also path-dependent, is similar to the material stress-strain relationship with stress-path dependence. However, the unloading part of the moment-curvature relationship of the beam section is elastic but not perfectly linear, although the unloading of both concrete and steel is assumed to be linearly elastic. It is also observed that when unloading happens, the variation of neutral axis depth has different trends for under- and over-reinforced sections. Moreover, even when the section is fully unloaded, there are still residual curvature and stress in the section in some circumstances. Various issues related to the post-peak behavior of reinforced concrete beams are also discussed.