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Won, Dae Yeon
- 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.
https://doi.org/10.14477/jhm.2021.34.2.055 인용 PDF KSCI

Tayebi, Akbar;Tabatabaeifar, Tayebeh;Peyghan, Esmaeil
- 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.
https://doi.org/10.4134/BKMS.2014.51.1.115 인용 PDF KSCI

Won, Dae Yeon
- 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.
https://doi.org/10.14477/jhm.2021.34.3.089 인용 PDF KSCI

PRADEEP KUMAR;AJAYKUMAR AR
- Honam Mathematical Journal
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- v.45 no.3
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- pp.491-502
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- 2023
As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.
https://doi.org/10.5831/HMJ.2023.45.3.491 인용 PDF