• Journal of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.869-893
• /
• 2016

We construct the extension of a hyperelliptic K3 surface to a Fano 6-fold with extraordinary properties in moduli. This leads us to a family of surfaces of general type with $p_g=1$, q = 0, $K^2=2$ and hyperelliptic canonical curve, each of which is a weighted complete inter-section inside a Fano 6-fold. Finally, we use these hyperelliptic surfaces to determine an 8-parameter family of Godeaux surfaces with ${\pi}_1={\mathbb{Z}}/2$.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.797-822
• /
• 2011

Log Enriques surface is a generalization of K3 and Enriques surface. We will classify all the rational log Enriques surfaces of rank 18 by giving concrete models for the realizable types of these surfaces.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.715-724
• /
• 2017

We study the Gauss map G of helicoidal surfaces in the 3-dimensional Euclidean space ${\mathbb{E}}^3$ with respect to the so called Cheng-Yau operator ${\square}$ acting on the functions defined on the surfaces. As a result, we completely classify the helicoidal surfaces with Gauss map G satisfying ${\square}G=AG$ for some $3{\times}3$ matrix A.

• 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.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.363-377
• /
• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized spherical curves in Euclidean (n + 1)-space ${\mathbb{E}}^{n+1}$. Further, we introduce some kind of generalized spherical surfaces in Euclidean spaces ${\mathbb{E}}^3$ and ${\mathbb{E}}^4$ respectively. We have shown that the generalized spherical surfaces of first kind in ${\mathbb{E}}^4$ are known as rotational surfaces, and the second kind generalized spherical surfaces are known as meridian surfaces in ${\mathbb{E}}^4$. We have also calculated the Gaussian, normal and mean curvatures of these kind of surfaces. Finally, we give some examples.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.149-156
• /
• 1998

We relate the existence of rational curves with the existence of rigid bundles of any even rank on Enriques surfaces and compare with the case of K3 surfaces.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1569-1578
• /
• 2015

We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3-space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

• 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 Chemical Society
• /
• v.30 no.4
• /
• pp.810-816
• /
• 2009

The interactions between four Keggin-type POMs (${SiW_{12}O_{40}}^{4-},\;{PW_{12}O_{40}}^{3-},\;{SiMo_{12}O_{40}}^{4-},\;and\;{PMo_{12}O_{40}}^{3-}$) and glassy carbon (GC) and highly oriented pyrolytic graphite (HOPG) surfaces are investigated in a systematic way. Electrochemical results show that molibdate series POMs adsorb relatively stronger than tungstate POMs on GC and HOPG surfaces. Adsorption of POMs on HOPG electrode surfaces is relatively stronger than on GC surfaces. ${SiMo_{12}O_{40}}^{4-}$ species exhibits unique adsorption behaviors on HOPG surfaces. Surface-confined ${SiMo_{12}O_{40}}^{4-}$ species on HOPG surfaces exhibit unique adsorption behaviors and inhibit the electron transfer from the solution phase species. The catalytic activity of the surface-confined POMs for hydrogen peroxide electroreduction is also examined, where ${PW_{12}O_{40}}^{3-}$ species adsorbed on GC surfaces exhibits the highest catalytic efficiency among the investigated POM modified electrode systems.

• Honam Mathematical Journal
• /
• v.38 no.3
• /
• pp.593-611
• /
• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.