• 대한수학회보
• /
• 제35권3호
• /
• pp.563-570
• /
• 1998

We makes an explicit description of compact 4-dimensional nilmanifolds as principal torus bundles and show that they are sysmplectic. We discuss some consequences of this and give in particular a Seibebrg-Witten-invariant proof of a Grovmov-Lawson theorem that if a compact 4-dimensional nilmanifold admits a metric of zero scalar curvature, then it is diffeomorphic to 4-tours, $T^4$.

• 호남수학학술지
• /
• 제38권2호
• /
• pp.305-316
• /
• 2016

In this paper we study general rotational surfaces in the 4-dimensional Euclidean space $\mathbb{E}^4$ and give a characterization of flat general rotational surface with pointwise 1-type Gauss map. Also, we show that a flat general rotational surface with pointwise 1-type Gauss map is a Lie group if and only if it is a Clifford torus.

• Korean Journal of Mathematics
• /
• 제6권2호
• /
• pp.313-318
• /
• 1998

In this paper we prove two independent theorems concerning formality of a nilmanifold and a differential graded algebra using the well-known theorem of Deligne-Griffiths-Morgan-Sullivan. We first give a rational homotopy theoretic proof to the statement that a nilmanifold is formal if and only if it is a torus. And then we study some conditions with which formality of one dga implies formality of the other in an extension of dga's.

• 한국정보과학회:학술대회논문집
• /
• 한국정보과학회 2002년도 봄 학술발표논문집 Vol.29 No.1 (A)
• /
• pp.697-699
• /
• 2002

임베딩은 어떤 연결망이 다른 연결망 구조에 포함 흑은 어떻게 연관되어 있는지를 알아보기 위해 어떤 특정한 연결망을 다른 연결망에 사상하는 것으로, 특정한 연결망에서 사용하던 여러 가지 알고리즘을 다른 연결망에서 효율적으로 이용할 수 있도록 한다. 본 논문에서는 2$^{2n-k}$ $\times$2$^{k}$ 토러스를 HCN(n,n)에 연장율 3에 임베딩 가능함을 보인다.

• 대한수학회보
• /
• 제52권1호
• /
• pp.313-321
• /
• 2015

In this paper, we construct infinite families of knots in $S^3$ which admit Dehn surgery producing a Seifert-fibered space over $S^2$ with four exceptional fibers. Also we show that these knots are turned out to be satellite knots, which supports the conjecture that no hyperbolic knot in $S^3$ admits a Seifert-fibered space over $S^2$ with four exceptional fibers as Dehn surgery.

• 대한수학회보
• /
• 제47권3호
• /
• pp.541-549
• /
• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• 대한수학회지
• /
• 제33권3호
• /
• pp.469-479
• /
• 1996

Toric variety is a normal algebraic variety containing algebraic torus $T_N$ as an open dense subset with an algebraic action of $T_N$ which is an extension of the group law of $T_N$. A toric variety can be described in terms of a certain collection, which is called a fan, of cones. From this fact, the properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. That is, we can translate the diffcult algebrogeometric properties of toric varieties into very simple properties about the combinatorics of cones in affine spaces over the reals.

• Journal of applied mathematics & informatics
• /
• 제9권2호
• /
• pp.621-633
• /
• 2002

This paper provides some functional equations and parametric expressions of f-essential maps on the projective plane, on the torus and on the Klein bottle with the size as a parameter and gives their explicit formulae for exact enumeration further.

• 대한수학회보
• /
• 제51권2호
• /
• pp.567-577
• /
• 2014

In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form $\mathbb{M}^{n+1}(c)$ (c = 1, 0,-1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in $\mathbb{S}^{n+1}(1)$ with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.

• Korean Journal of Mathematics
• /
• 제16권1호
• /
• pp.1-24
• /
• 2008

Let $Lu=u_{tt}+u_{xxxx}$ and E be the complete normed space spanned by the eigenfunctions of L. We reveal the existence of six nontrivial solutions of a nonlinear suspension bridge equation $Lu+bu^+=1+{\epsilon}h(x,t)$ in E when the nonlinearity crosses three eigenvalues. It is shown by the critical point theory induced from the limit relative category of the torus with three holes and finite dimensional reduction method.