• Bulletin of the Korean Mathematical Society
• /
• v.50 no.4
• /
• pp.1329-1343
• /
• 2013

In this paper, we define translation surfaces in the 3-dimensional Heisenberg group $\mathcal{H}_3$ obtained as a product of two planar curves lying in planes, which are not orthogonal, and study minimal translation surfaces in $\mathcal{H}_3$.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.135-142
• /
• 2013

In the present paper, we discuss the rigidity phenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

• East Asian mathematical journal
• /
• v.40 no.3
• /
• pp.287-293
• /
• 2024

For a nondegenerate irreducible projective variety, it is a classical problem to describe its defining equations and the syzygies among them. In this paper, we precisely determine a minimal generating set and the minimal free resolution of defining ideals of some rational curves of maximal genus in ℙ³.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1707-1714
• /
• 2016

Let $C{\subset}{\mathbb{P}}^r$ be a nondegenerate projective curve of degree d > r + 1 and of maximal regularity. Such curves are always contained in the threefold scroll S(0, 0, r - 2). Also some of such curves are even contained in a rational normal surface scroll. In this paper we study the minimal free resolution of the homogeneous coordinate ring of C in the case where $d{\leq}2r-2$ and C is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of C explicitly.

• Journal of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.407-442
• /
• 2007

The study of Euclidean submanifolds with finite type "classical" Gauss map was initiated by B.-Y. Chen and P. Piccinni in [11]. On the other hand, it was believed that for spherical sub manifolds the concept of spherical Gauss map is more relevant than the classical one (see [20]). Thus the purpose of this article is to initiate the study of spherical submanifolds with finite type spherical Gauss map. We obtain several fundamental results in this respect. In particular, spherical submanifolds with 1-type spherical Gauss map are classified. From which we conclude that all isoparametric hypersurfaces of $S^{n+1}$ have 1-type spherical Gauss map. Among others, we also prove that Veronese surface and equilateral minimal torus are the only minimal spherical surfaces with 2-type spherical Gauss map.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.113-122
• /
• 2023

We classify lens spaces with the Milnor fillable contact structure that admit minimal symplectic fillings whose second Betti numbers are one.

• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.13-33
• /
• 2006

In this article, we study the relations of horizontally conformal maps and harmonic morphisms with the stability of minimal fibers. Let ${\varphi}:(M^n,g){\rightarrow}(N^m,h)$ be a horizontally conformal submersion. There is a tensor T measuring minimality or totally geodesics of fibers of ${\varphi}$. We prove that if T is parallel and the horizontal distribution is integrable, then any minimal fiber of ${\varphi}$ is volume-stable. As a corollary, we obtain that any fiber of a submersive harmonic morphism whose fibers are totally geodesics and the horizontal distribution is integrable is volume-stable. As a consequence, we obtain if ${\varphi}:(M^n,g){\rightarrow}(N^2,h)$ is a submersive harmonic morphism of minimal fibers from a compact Riemannian manifold M into a surface N, T is parallel and the horizontal distribution is integrable, then ${\varphi}$ is energy-stable.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.531-540
• /
• 2016

In this work, we introduce the complete Riemannian manifold $\mathbb{F}_3$ which is a three-dimensional real vector space endowed with a conformally flat metric that is a solution of the Einstein equation. We obtain a second order nonlinear ordinary differential equation that characterizes the helicoidal minimal surfaces in $\mathbb{F}_3$. We show that the helicoid is a complete minimal surface in $\mathbb{F}_3$. Moreover we obtain a local solution of this differential equation which is a two-parameter family of functions ${\lambda}_h,K_2$ explicitly given by an integral and defined on an open interval. Consequently, we show that the helicoidal motion applied on the curve defined from ${\lambda}_h,K_2$ gives a two-parameter family of helicoidal minimal surfaces in $\mathbb{F}_3$.

• Restorative Dentistry and Endodontics
• /
• v.14 no.2
• /
• pp.1-4
• /
• 1989

To determine the thickness of coronal hard structure the minimal distance between pupal surface and outer surface of crown was measured by means of Bowley gauge on extracted first molars. Upper(28 teeth) and lower(24 teeth) were carefully collected from 30-39 years of age and male. The teeth were split mesio-distally through central pit. On the split surface various part which are deeply related in cavity preparation were measured (schematic drawing). The results were as follows: A : Distance from mesio-cervical enamel to pulp chamber surface. upper $2.63{\pm}0.19$(mm) Lower $2.18{\pm}0.27$(um) B : Distance from mesial chamber ceiling to mesial surface upper $2.75{\pm}0.34$ Lower $2.62{\pm}0.31$ C : Distance from mesial chamber ceiling to occlusal surface upper $3.82{\pm}0.51$ Lower $3.49{\pm}0.50$ D : Distance from distal chamber ceiling to occlusal surface upper $4.28{\pm}0.69$ Lower $3.90{\pm}0.52$ E : Distance from distal chamber ceiling to distal surface upper $2.79{\pm}0.45$ Lower $2.41{\pm}0.40$ F : Distance from disto cervical enamel to pulp chamber surface upper $2.49{\pm}0.24$ Lower $2.39{\pm}0.25$.

• The Korean Journal of Physiology
• /
• v.5 no.1
• /
• pp.51-58
• /
• 1971

In an attempt to further clarify the effect of X·irradiation on the activity of surfactant in rabbits, X-ray in dose of 900r was irradiated to the lung tissues of rabbits in vitro. Tension-area diagram of the lung extract was recorded automatically by a modified Langmuir-Wilhelmy balance with a synchronized recording system designed in this department. The surface tension of the lung extract was measured at 1,3,5,24 and 48 hours post-irradiation, and the results were compared with the non·irradiated normal group. The result$ thus obtained are summarized as follows: I The maximal surface tension, minimal surface tension, width of the tension·area diagram at the surface area of 40% in the lung extract and stability index of the normal rabbit long extract were 40.73 dynes/cm, 8.96 dynes/cm, 20.71 dynes/cm and 1.28, respectively. II. When 900r of X-ray was irradiated to the lung in vitro, 1) The maximal and minimal surface tensions did not differ noticeably from the normal at 1,3, and 5 post-irradiation hours, but the minimal surface tension increased significantly at 24 and 48 hours Post-irradiation. 2) The width of the tension area at the surface area of 40% showed a tendency of decrease throughout the experiment. 3) The stability index showed no significant change at 1,3 and 5 post-irradiation hours,but at 24 and 48 hours post-irradiation a significant decrease was observed comparing with the control. III. Activity of surfactant was significantly depressed by X·irradiation in vitro especially at 24 and 48 hours post-irradiation.