• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1291-1312
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• 2007

We study some extremal problems on the Cartan-Hartogs domains. Through computing the minimal circumscribed Hermitian ellipsoid of the Cartan-Hartogs domains, we get the $Carath\acute{e}odory$ extremal mappings between the Cartan-Hartogs domains and the unit hyperball, and the explicit formulas for computing the $Carath\acute{e}odory$ extremal value.

• East Asian mathematical journal
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• v.35 no.5
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• pp.529-534
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• 2019

The purpose of this article is to present The $Carath{\acute{e}}odory$-Cartan-Kaup-Wu theorem for connected Kobayashi hyperbolic almost complex manifolds.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1683-1698
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• 2017

In this paper, we study the $Carath{\acute{e}}odory$ extremal problems on the Hua domain of the first three types. We give the explicit formula for the $Carath{\acute{e}}odory$ extremal problems between the first three types of Hua domain and the unit ball, which improves the works done on Hua domain and Cartan-egg domain and super-Cartan domain.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.13-26
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• 2009

Elie Cartan is one of the mathematicians whose works marked the development of geometry and algebra of 20th century. We illuminate his mathematical contributions which is familiar to the experts but is alien to most of the mathematicians in general. Also we elucidate some of his influences.

• Journal for History of Mathematics
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• v.32 no.1
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• pp.1-15
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• 2019

We divide the timeline of the history of Finsler geometry, which dates back to Riemann's inaugural lecture in 1854, into three periods (hibernation, hiatus, rebirth) and we study formation of Romanian Finsler school around Iasi, Romania during the hiatus period. We look for the history centered around Radu Miron who is a third generation geometer of Iasi University and the mathematical heritage there through five generations. We also investigate mathematical impact of T. Levi-Civita, D. Hilbert, ${\acute{E}}$ Cartan who are considered as top mathematicians at their time.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.47-59
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• 2018

We define the $e^{\alpha}_1e^{\alpha}_3$-isotropic Smarandache curves of type-1 and type-2, the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_3$-isotropic Smarandache curve, and the $e^{\alpha}_1e^{\alpha}_2e^{\alpha}_4$-isotropic Smarandache curves of type-1 and type-2. Then we examine these kinds of isotropic Smarandache curve according to Cartan frame in the complex 4-space $\mathbb{C}^4$ and give some differential geometric properties of these Samarandache curves.

• Journal for History of Mathematics
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• v.34 no.3
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• pp.89-111
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• 2021

This paper is a continuation of the study on the history of the Japanese school of Finsler geometry. We had studied on the birth of Japanese school of Finsler geometry. In this paper, we find out what motivated Japanese to embrace Finsler geometry and we collect the history and analyze trends of Japanese school of Finsler geometry since its founding by M. Matsumoto.