• 호남수학학술지
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• 제36권4호
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• pp.739-753
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• 2014

In this study, it is aimed to analyze how relationship among Blaschke vectors that the obtained formulae in [2, 3] change if parameter ruled surfaces of the spacelike line congruence are not choosed as principle ruled surfaces. Moreover, using the relation among Blaschke vectors, we obtain Manheim's and Liouville's formulae. This new method can be applied to congruences. Thus, we can obtain new formulae in lines space.

• 대한수학회보
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• 제50권6호
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• pp.1781-1797
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• 2013

Let x : $M{\rightarrow}\mathbb{R}^n$ be an n - 1-dimensional hypersurface in $\mathbb{R}^n$, L be the Laguerre Blaschke tensor, B be the Laguerre second fundamental form and $D=L+{\lambda}B$ be the Laguerre para-Blaschke tensor of the immersion x, where ${\lambda}$ is a constant. The aim of this article is to study Laguerre Blaschke isoparametric hypersurfaces and Laguerre para-Blaschke isoparametric hypersurfaces in $\mathbb{R}^n$ with three distinct Laguerre principal curvatures one of which is simple. We obtain some classification results of such isoparametric hypersurfaces.

• 대한수학회지
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• 제46권1호
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• pp.151-170
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• 2009

Let m be a positive integer. We show that for any given real number ${\alpha}\;{\in}\;[0,\;1]$ and complex number $\mu$ with $|\mu|{\leq}1$ which satisfy $e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\alpha$. Moreover if the given real number $\alpha$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.

• East Asian mathematical journal
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• 제21권1호
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• pp.123-135
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• 2005

We have extended the $H^p$ space and estabilished the derivative of inner functions, Blaschke product on weighted Hardy spaces for the unit disc in complex plane.

• 대한수학회지
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• 제31권3호
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• pp.393-400
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• 1994

Subminifolds of Euclidean spaces have been studied by examining geodesics of the submanifolds viewed as curves of the ambient Euclidean spaces ([3], [7], [8], [9]). K.Sakamoto ([7]) studied submanifolds of Euclidean space whose geodesics are plane curves, which were called submanifolds with planar geodesics. And he completely calssified such submanifolds as either Blaschke manifolds or totally geodesic submanifolds. We now ask the following: If there is a point p of the given submanifold in Euclidean space such that every geodesic of the submanifold passing through p is a plane curve, how much can we say about the submanifold\ulcorner In the present paper, we study submanifolds of euclicean space with such property.

• 대한수학회지
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• 제43권3호
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• pp.593-607
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• 2006

In this paper, we study the properties of the dual harmonic quermassintegrals systematically and establish some inequalities for the dual harmonic quermassintegrals, such as the Minkowski inequality, the Brunn-Minkowski inequality, the Blaschke-Santalo inequality and the Bieberbach inequality.

• 대한수학회지
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• 제44권2호
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• pp.297-306
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• 2007

In this paper, we present a new kind of duality between intersection bodies and projection bodies. Furthermore, we establish some counterparts of dual Brunn-Minkowski inequalities for intersection bodies.

• Kyungpook Mathematical Journal
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• 제26권1호
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• pp.1-3
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• 1986

• 충청수학회지
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• 제33권1호
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• pp.1-7
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• 2020

In this paper, it is shown that the reversible harmonic Finsler metrics on spheres must be Riemannian.

• 호남수학학술지
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• 제32권4호
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.