• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.501-513
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• 2003

The Matsumoto metric is an ($\alpha,\;\bata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\mid$\beat$\mid$\;<\;$\mid$\alpha$\mid$$ by the first author. He introduced an approximate Matsumoto metric as the ($\alpha,\;\bata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

• East Asian mathematical journal
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• v.17 no.2
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• pp.325-337
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• 2001

We consider the special hypersurface of the first approximate Matsumoto metric with $b_i(x)={\partial}_ib$ being the gradient of a scalar function b(x). In this paper, we consider the hypersurface of the first approximate Matsumoto space with the same equation b(x)=constant. We are devoted to finding the condition for this hypersurface to be a hyperplane of the first or second kind. We show that this hypersurface is not a hyper-plane of third kind.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.153-163
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• 2002

The present paper is devoted to studying the condition for a Finsler space with the second approximate Matsumoto metric to be a Berwald space and to be a Douglas space.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.209-221
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• 2008

In the present paper, first we define a Douglas space of the second kind of a Finsler space with an (${\alpha},{\beta}$)-metric. Next we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a Douglas space of the second kind and the Finsler space with a Matsumoto metric be a Douglas space of the second kind.

• Journal for History of Mathematics
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• v.34 no.2
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• pp.55-74
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• 2021

Matsumoto Makoto is regarded as founding father of the Japanese school of Finsler geometry because he established the Japanese Society of Finsler Geometry in 1968 and organized the Symposium every year since then. In this paper, we investigate how Matsumoto initiated the study of this topic leaping over geographical limit and how Yano Kentaro and Kawaguchi Akitsugu had affected Matsumoto in the formation of the Japanese school of Finsler geometry. We also take a view of the role of É. Cartan who invented the concept of the connection in early 20th century in this regard.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1996.10a
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• pp.76-79
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• 1996

최근 주로 일본 해안공학자인 Hattori와 Matsumoto(1977), Aoyama 등(1900), Yu 등(1990)에 의하여 잠재평판(submerged plate)이 항만의 외곽 구조물로서 파랑 에너지의 저감에 미치는 영향에 대한 연구가 수행되어 왔다. Hattori와 Matsumoto(1977)에 의하면 장파에 대하여 평판구조물은 방파제로서의 역할을 못하는 것으로 판명됐으며 그리고 Yu 등(1990)의 실험결과에 의하면 평판의 길이가 전수심에 의한 파장과 동일하고 핑판위의 수심이 전수심의 0.2인 경우 0.8초의 단파에 대하여 투과율이 30%까지 감소되었다. (중략)

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.115-128
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• 2014

In this paper, we study the second approximate Matsumoto metric F = ${\alpha}+{\beta}+{\beta}^2/{\alpha}+{\beta}^3/{\alpha}^2$ on a manifold M. We prove that F is of scalar flag curvature and isotropic S-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.81-89
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• 2012

In the present paper, we nd the conditions to characterize projective change between two (${\alpha}$, ${\beta}$)-metrics, such as Matsumoto metric $L=\frac{{\alpha}^2}{{\alpha}-{\beta}}$ and Randers metric $\bar{L}=\bar{\alpha}+\bar{\beta}$ on a manifold with dim $n$ > 2, where ${\alpha}$ and $\bar{\alpha}$ are two Riemannian metrics, ${\beta}$ and $\bar{\beta}$ are two non-zero 1-formas.

• Bulletin of the Korean Mathematical Society
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• v.13 no.2
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• pp.121-125
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• 1976

• Journal of the Korean Mathematical Society
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• v.21 no.1
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• pp.49-61
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• 1984