Book Review
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MathSciNet review:
1567966
Full text of review:
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Book Information:
Author:
Aurel Bejancu
Title:
Finsler geometry and applications
Additional book information:
Ellis Horwood Limited, Chichester, 1990, 198 pp., US$59.50. ISBN 0-13-317975-3.
G. S. Asanov, Finsler geometry, relativity and gauge theories, Fundamental Theories of Physics, D. Reidel Publishing Co., Dordrecht, 1985. MR 827217, DOI 10.1007/978-94-009-5329-1
[2] L. Berwald, Über Parallelübertragung in Räumen mit allgemeiner Massbestimmung, Jahresber. Deutsch. Math.-Ver. 34 (1926), 213-220.
[3] C. Carathéodory, Über die diskontinuierlichen Lösungen in der Variationsrechnung, Dissertation, Göttingen, 1904, Collected Works, vol. 1, C. H. Beck, München, 1954, pp. 3-79.
C. Carathéodory, Über die starken maxima und minima bei einfachen Integralen, Math. Ann. 62 (1906), no. 4, 449–503 (German). MR 1511387, DOI 10.1007/BF01449816
[5] E. Cartan, Les espaces de Finsler, Actualités Sci. Indust. 79 (1934).
P. Finsler, Über Kurven und Flächen in allgemeinen Räumen, Verlag Birkhäuser, Basel, 1951 (German). MR 0042195
Makoto Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha Press, Shigaken, 1986. MR 858830
[8] B. Riemann, Über die Hypothesen, welche der Geometrie zugrunde liegen, Habilitationsschrift, Göttingen, 1854. Collected Works, Dover Publications, NY, 1953, pp. 272-287.
Hanno Rund, Differentsial′naya geometriya finslerovykh prostranstv, “Nauka”, Moscow, 1981 (Russian). Translated from the English by G. S. Asanov. MR 641695
Hanno Rund, Direction-dependent connection and curvature forms, Abh. Math. Sem. Univ. Hamburg 50 (1980), 188–209. MR 593750, DOI 10.1007/BF02941428
- [1]
- G. S. Asanov, Finsler geometry, relativity, and gauge theories, Reidel Publishing Co., Dordrecht, 1985. MR 827217 (87d:53122)
- [2]
- L. Berwald, Über Parallelübertragung in Räumen mit allgemeiner Massbestimmung, Jahresber. Deutsch. Math.-Ver. 34 (1926), 213-220.
- [3]
- C. Carathéodory, Über die diskontinuierlichen Lösungen in der Variationsrechnung, Dissertation, Göttingen, 1904, Collected Works, vol. 1, C. H. Beck, München, 1954, pp. 3-79.
- [4]
- -, Über die starken Maxima and Minima bei einfachen Integralen, Math. Ann. 62 (1906), 449-503. Collected Works, vol. 1, C. H. Beck, München, 1954, pp. 80-142. MR 1511387
- [5]
- E. Cartan, Les espaces de Finsler, Actualités Sci. Indust. 79 (1934).
- [6]
- P. Finsler, Über Kurven and Flächen in allgemeinen Räumen, Dissertation, Göttingen, 1918. Reprinted by Birkhäuser Verlag, Basel, 1951. MR 0042195 (13:74d)
- [7]
- M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseicha Press, Ōtsu, 1986. MR 858830 (88f:53111)
- [8]
- B. Riemann, Über die Hypothesen, welche der Geometrie zugrunde liegen, Habilitationsschrift, Göttingen, 1854. Collected Works, Dover Publications, NY, 1953, pp. 272-287.
- [9]
- H. Rund, The differential geometry of Finsler spaces, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959; (Russian Translation by G. S. Asanov, Nauka, Moscow, 1981). MR 641695 (83i:53097)
- [10]
- -, Direction-dependent connection and curvature forms, Abh. Math. Sem. Univ. Hamburg 50 (1980), 188-209. MR 593750 (81m:53036)
Review Information:
Reviewer:
Hanno Rund
Journal:
Bull. Amer. Math. Soc.
26 (1992), 148-151
DOI:
https://doi.org/10.1090/S0273-0979-1992-00235-5
