• Communications of the Korean Mathematical Society
• /
• v.10 no.3
• /
• pp.545-560
• /
• 1995

In this paper, we show one family of normal quintic surfaces in $P^3$ which are birationally isomorphic to Enriques surfaces. We prove that the dimension of the moduli space of these Enriques surfaces is 6.

• Journal of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.545-566
• /
• 1999

In this paper we describe normal quintic surfaces in P which are birationally isomorphic to Enriques surfaces. especially we characterize the sublinear systems which give rise to one of two Stagnaro's normal quintic surfaces in P3.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.6
• /
• pp.2035-2045
• /
• 2015

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with special invariants. In the present paper we give the complete classification of Chen meridian surfaces and meridian surfaces with parallel normal bundle.

• Honam Mathematical Journal
• /
• v.44 no.2
• /
• pp.259-270
• /
• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.

• The korean journal of orthodontics
• /
• v.18 no.1 s.25
• /
• pp.165-173
• /
• 1988

The purpose of this study was to investigate and evaluate what proportion is the characteristics in Korean dental arches with normal occlusion. Many others have already indicated Golden proportion in normal dental arches, but have not considered any racial and sociocultural differences. So the author postulated $(\sqrt{2})^n$ relations in Koreans. The materials were consisted of 134 dental casts with normal occlusion, which have never undergone orthodontic and prosthodontic procedures. Measurements were made on the arch dimensions using sliding caliper and data were computerized. The findings were as follows: 1. The width between the distal surfaces of the upper centrals, had $(\sqrt{2})^3$ relation with the width between the buccal surfaces of the upper 1 st premolars in Koreans. 2. The width between the distal surfaces of the lower laterals had $(\sqrt{2})$ relation with the width between the distal surfaces of the lower canines, and had $(\sqrt{2})^2$ relation with the distal surfaces of the upper centrals. 3. The width between the distal surfaces of the lower centrals had $(\sqrt{2})^2$ relation with the width between the distal surfaces of the lower laterals, and had $(\sqrt{2})^3$ relation with the width between the distal surfaces of the upper centrals.

• Communications of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.189-200
• /
• 1999

In this paper, we proved that the only surfaces of 1-type Gauss map with flat normal connection are spheres, products of two plane circles and helical cylinders.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.301-312
• /
• 2015

In this paper, we study a class of spacelike rotational surfaces in the Minkowski 4-space $\mathbb{E}^4_1$ with meridian curves lying in 2-dimensional spacelike planes and having pointwise 1-type Gauss map. We obtain all such surfaces with pointwise 1-type Gauss map of the first kind. Then we prove that the spacelike rotational surface with flat normal bundle and pointwise 1-type Gauss map of the second kind is an open part of a spacelike 2-plane in $\mathbb{E}^4_1$.

• Korean Journal of Mathematics
• /
• v.25 no.4
• /
• pp.513-535
• /
• 2017

As a continuation to the study in [8, 12, 15, 17], we construct bi-conservative central normal (BCN) and bi-conservative asymptomatic normal (BAN) ruled surfaces in Euclidean 3-space ${\mathbb{E}}^3$. For such surfaces, local study is given and some examples are constructed using computer aided geometric design (CAGD).

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.7 s.184
• /
• pp.187-193
• /
• 2006

This paper introduces and illustrates the results of a new method for offsetting the triangular mesh generated from multiple surfaces. The meshes generated from each surface are separated each other and normal directions are different. The face normal vectors are flipped to upward and the lower faces covered by upper faces are deleted. The virtual normal vectors are introduced and used to of feet boundary. It was shown that new method is better than previous methods in offsetting the triangular meshes generated from multiple surfaces. The introduced offset method was applied for 3-axis tool path generation system and tested by NC machining.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.377-394
• /
• 2015

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B$\ddot{a}$cklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B$\ddot{a}$cklund transformations on Razzaboni surfaces commute.