• 호남수학학술지
• /
• 제31권2호
• /
• pp.177-183
• /
• 2009

In this article, we study ruled surfaces in a Lorentzian space-time, which have finite type immersion. We give a condition for bi-finite type surfaces to be of finite type.

• 대한수학회지
• /
• 제41권2호
• /
• pp.379-396
• /
• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• 대한수학회지
• /
• 제53권4호
• /
• 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 ${\pi}_1={\mathbb{Z}}/2$.

• 대한수학회논문집
• /
• 제35권1호
• /
• pp.251-260
• /
• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• 대한수학회보
• /
• 제52권1호
• /
• 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 $\mathbb{E}^4_1$.

• 대한수학회지
• /
• 제35권2호
• /
• pp.315-330
• /
• 1998

Chen and Piccinni [7] have classified all compact surfaces in a Euclidean space $R^{2＋p}$ with 1-type generalized Gauss map. Being motivated by this result, the purpose of this paper is to consider the Lorentz version of the classification theorem and to obtain a complete classification of space-like surfaces in indefinite Euclidean space $R_{p}$ $^{2＋p}$ with 1-type generalized Gauss map.p.

• 대한수학회보
• /
• 제53권2호
• /
• pp.519-530
• /
• 2016

In this paper, we study surfaces of revolution in the three dimensional pseudo-Galilean space. We classify surfaces of revolution generated by a non-isotropic curve in terms of the Gauss map and the Laplacian of the surface. Furthermore, we give the classification of surfaces of revolution generated by an isotropic curve satisfying pointwise 1-type Gauss map equation.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.581-590
• /
• 2018

In this paper, we consider surfaces in the 3-dimensional Euclidean space $\mathbb{E}^3$ which are of finite III-type, that is, they are of finite type, in the sense of B.-Y. Chen, corresponding to the third fundamental form. We present an important family of surfaces, namely, tubes in $\mathbb{E}^3$. We show that tubes are of infinite III-type.

• 대한수학회논문집
• /
• 제18권2호
• /
• pp.289-295
• /
• 2003

In this paper, we study ruled surfaces in Minkowski space, which admit 1-type Gauss map. In particular, non-cylindrical ruled surfaces with finite type Gauss map are of k-type (k $\geq$ 2).

• 한국진공학회:학술대회논문집
• /
• 한국진공학회 2016년도 제50회 동계 정기학술대회 초록집
• /
• pp.157.2-157.2
• /
• 2016

Water repellent surfaces may enhance the condensation by efficiently removing the condensed droplets. However, such surfaces may lose their original performance as they are exposed to external mechanical stresses. In this work, we fabricated spray-coated mechanically robust superhydrophobic surfaces using treated titanium dioxide (Type 1) or silica particles (Type 2). Then we compared the mechanical robustness of such surfaces with the silane-coated superhydrophobic surface and PEEK coated surface using a controlled-sand blasting method. The results show that the spray-coated samples can maintain the same level of the contact angle hysteresis than silane-coated superhydorphobic surface after sand blasting at 2 bar. The spray-coating method was applied to the tube type condenser and the condensation behaviors were observed within the environmental chamber with controlled pressure, humidity and non-condensable gas. Previously-reported droplet jumping was observed in the early stage of the condensation event, but soon the droplet jumping stopped and only dropwise condensation was observed since the condensed droplets were pinned on the cracks at spray-coated surfaces. The static contact angle decreases from $158.0^{\circ}$ to $133.2^{\circ}$, and hysteresis increases from $3.0^{\circ}$ to $23.5^{\circ}$ when active condensation occurs on such surfaces. This work suggests the benefits and limitation of spray-coated superhydrophobic condensers and help develop advanced condensers for practical use.