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http://dx.doi.org/10.14477/jhm.2021.34.3.089

On the history of 60 years of Japanese School of Finsler Geometry  

Won, Dae Yeon (Dept. of Math. Duksung Women's Univ.)
Publication Information
Journal for History of Mathematics / v.34, no.3, 2021 , pp. 89-111 More about this Journal
Abstract
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.
Keywords
K. Yano; A. Kawaguchi; M. Matsumoto; ${\acute{E}}$. Cartan; Finsler geometry; Japanes school of Finsler geometry;
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  • Reference
1 Y. Muto and K. Yano, Homogeneous contact manifolds and almost Finsler manifolds, Kodai Math. Sem. Rep. 21 (1969), 16-45.   DOI
2 E. Cartan, Les groupes d'holonomie des espaces generalises, Acta Mathematica 48 (1926), 1-42.   DOI
3 E. Cartan, Les espaces de Finsler, Actual. Sci. Ind., no. 79, Herman, 1934.
4 S. S. Chern, On Finsler Geometry, C. R. Acad. Sci. Paris Ser. I Math. 314 (1992), 757-761.
5 E. T. David and K. Yano, On the connection in Finsler space as an induced connection, Rend. Circ. Mat. Palermo 3 (1954), 409-417.   DOI
6 E. T. David and K. Yano, On the tangent bundles of Finsler and Riemannian manifolds, Rend. Circ. Mat. Palermo 12 (1963), 211-228.   DOI
7 M. Haimovici, Le parallelisme dans les espaces de Finsler et la differentialtion invariante de T. Levi-Civita, Ann. Sci. Univ. Iasi Ser. I. 24 (1938), 214-218.
8 A. Kawaguchi, Theory of connections in the generalized Finsler manifold, Proc. Imp. Acad. 7(6) (1931), 211-214.   DOI
9 M. Matsumoto, Theory of Finsler spaces and differential geometry of tangent bundles, J. Math. of Kyoto Univ. 7 (1967), 169-204.
10 Won D. Y., On the Beginning of the Formation of Japanese School of Finsler Geometry, submitted.
11 K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953.
12 K. Yano and S. Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc., New York, 1973.
13 K. Yano, 接続の幾何学(접속의 기하학), 数学ライブラリー(수학 라이브러리) No. 32, Morikita Publishing, Tokyo, Japan, 1947.
14 MathSciNet 수학넷, https://mathscinet.ams.org/mathscinet.
15 E. Cartan, Sur un probleme d'equivalence et la theorie des espaces metrique generalises, Math. Cluj 4 (1930), 114-136.
16 E. Cartan, Sur les espaces de Finsler, C. R. Acad. Sci. Paris Ser. I Math. 196 (1933), 582-586.
17 S. S. Chern, Local Equivalence and Euclidean Connections in Finsler Spaces, Sci. Rep. Nat. Tsing Hua Univ. Ser. A 5 (1948), 95-121.
18 A. Kawaguchi, Theory of connections in the generalized Finsler manifold, II, Proc. Imp. Acad. 8(8) (1932), 340-343.   DOI
19 A. Kawaguchi, Geometry in an n-Dimensional Space With the Arc Length, Transactions of the American Mathematical Society 44(2) (1938), 153-167.   DOI
20 M. Matsumoto, A Finsler connection with many torsions, Tensor, N. S. 17 (1966), 217-226.
21 M. Matsumoto, Connections, metrics and almost complex structures of tangent bundles, J. Math. of Kyoto Univ. 5 (1966), 251-278.
22 M. Matsumoto, A global foundation of Finsler Geometry, Memo. Coll. Sci. Univ. of Kyoto A 33 (1960/61), 171-208.
23 M. Matsumoto, Metrical Differential Geometry (Japanese), Kiso- Sugaku-Sensho, Shokabo, 1975.
24 S. Sabau and H. Shimada, Finsler Geometry, Sapporo 2005 - In Memory of Makoto Matsumoto, Advanced Studies in Pure Mathematics 48 (2007), Mathematical Society of Japan.
25 Won D. Y., On the History of Formation of Romanian School of Finsler Geometry, Journal for History of Mathematics 32(1) (2019), 1-15. 원대연, 루마니아 핀슬러 기하학파 형성의 역사, Journal for History of Mathematics 32(1) (2019), 1-15.   DOI
26 T. Okubo and K. Yano, On tangent bundles with Sasakian metrics of Finslerian and Riemannian manifolds, Ann. Mat. Pura. Appl. 87(4) (1970), 137-162.   DOI
27 Wikipedia 위키백과, http://en.wikipedia.org/wiki.
28 K. Yano, Les espaces a connexion projective et la geometrie projective, Analele S fftiin fftifice ale Universita fftii "Al. I. Cuza" din Ias ffi 24 (1938), 395-464.
29 K. Yano, On harmonic and Killing vector fields, Ann. of Math. 55(2) (1952), 38--45.   DOI
30 M. Matsumoto, Foundations of Finsler Geometry and special Finsler spaces, Kasheisha Press, 1986.