• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.87-93
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• 1998

Mejia and Minda proved that if a hyperbolic simply connected region $\Omega$ is k-convex, then (equation omitted), $z \in \Omega$. We show that this inequality actually characterizes k-convex regions.

• 통합자연과학논문집
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• 제10권2호
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• pp.110-114
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• 2017

The connected and simply connected four-dimensional matrix solvable Lie group $Sol^4_1$ is the four-dimensional geometry. A crystallographic group of $Sol^4_1$ is a discrete cocompact subgroup of $Sol^4_1{\rtimes}D(4)$. In this paper, we geometrically describe the crystallographic groups of $Sol^4_1$.

• 대한수학회지
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• 제57권4호
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• pp.973-986
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• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• 대한수학회보
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• 제44권1호
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• pp.103-108
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• 2007

In this paper, we obtain some lower bounds for area of non-simply connected compact singular surfaces of nonpositive curvature. One inequality involves systole and area of the surface.

• Korean Journal of Mathematics
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• 제6권2호
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• pp.137-148
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• 1998

We briefly discuss the Lie groups, it's nilpotency and representations of a nilpotent Lie groups. Dixmier and Kirillov proved that simply connected nilpotent Lie groups over $\mathbb{R}$ are monomial. We reformulate the above result at the Lie algebra level.

• 대한수학회논문집
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• 제21권1호
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• pp.151-163
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• 2006

Any simply connected fixed point cohomogeneity one riemannian manifold with positive sectional curvature is diffeomorphic to one of the compact rank one symmetric spaces.

• 대한수학회지
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• 제50권3호
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• pp.493-507
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• 2013

We construct a new family of simply connected minimal complex surfaces of general type with $p_g$ = 1, $q$ = 0, and $K^2$ = 3, 4, 5, 6, 8 using a $\mathbb{Q}$-Gorenstein smoothing theory.

• 대한수학회논문집
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• 제10권3호
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• pp.699-705
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• 1995

We first generalize the Volodin space which Volodin constructed in order to define a new algebraic K-theory. We investigate the topological (homotopy) properties of the general Volodin space. We also provide a theorem which seems to be useful in pure homotopy theory. We prove that $V(*_\alpha G_\alpha, {G_\alpha})$ is simply connected.

• 대한수학회지
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• 제32권4호
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• pp.835-848
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• 1995

Let $M_n$(c) be an n-dimensional complete and simply connected Kahlerian manifold of constant holomorphic sectional curvature c, which is called a complex space form. Then according to c > 0, c = 0 or c < 0 it is a complex projective space $P_nC$, a complex Euclidean space $C^n$ or a complex hyperbolic space $H_nC$.

• 대한수학회보
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• 제36권4호
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• pp.701-706
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• 1999

A characterization of geodesic spheres in the simply connected space forms in terms of the ratio of the Gauss-Kronecker curvature and the (usual) mean curvature is given: An immersion of n dimensional compact oriented manifold without boundary into the n + 1 dimensional Euclidean space, hyperbolic space or open half sphere is a totally umbilicimmersion if the mean curvature $H_1$ does not vanish and the ratio $H_n$/$H_1$ of the Gauss-Kronecker curvature $H_n$ and $H_1$ is constant.