Abstract
In this chapter, we study Berwald spaces in some detail. Here are several reasons why such spaces are so important. These reasons are elaborated upon as the chapter unfolds.
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References
P. L. Antonelli, R. S. Ingarden, and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, FTPH 58, Kluwer Academic Publishers, 1993.
D. Bao and S. S. Chern, A note on the Gauss-Bonnet theorem for Finsler spaces, Ann. Math. 143 (1996), 233–252.
D. Bao, S. S. Chern, and Z. Shen, On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces, Cont. Math. 196 (1996), 15–25.
L. Berwald, Two-dimensional Finsler spaces with rectilinear extremals, Ann. Math. 42 (1941), 84–112.
S. S. Chern, A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. Math. 45(4) (1944), 747–752.
S. S. Chern, On the curvatura integra in a Riemannian manifold, Ann. Math. 46(4) (1945), 674–684.
M. Hashiguchi and Y. Ichijyō, On some special (α, β)-metrics, Rep. Fac. Sci. Kagoshima Univ. 8 (1975), 39–46.
Y. Ichijyō, Finsler manifolds modeled on a Minkowski space, J. Math. Kyoto Univ. (Kyoto Daigaku J. Math.) 16-23 (1976), 639–652.
S. Kikuchi, On the condition that a space with (α, β)-metric be locally Minkowskian, Tensor, N.S. 33 (1979), 242–246.
M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Japan, 1986.
M. Matsumoto, On Finsler spaces with Randers’ metric and special forms of important tensors, J. Math. Kyoto Univ. (Kyoto Daigaku J. Math.) 14 (1974), 477–498.
M. Matsumoto, Theory of Finsler spaces with m-th root metric II, Publ. Math. Debr. 49 (1996), 135–155.
K. Okubo, Lecture at the Symposium on Finsler Geometry, 1977, unpublished (communicated to us by M. Matsumoto).
H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, 1959.
C. Shibata, H. Shimada, M. Azuma, and H. Yasuda, On Finsler spaces with Randers’ metric, Tensor, N.S. 31 (1977), 219–226.
M. Spivak, Differential Geometry, vol. II, Publish or Perish, 1970.
Z. Szabó, Positive definite Berwald spaces (structure theorems on Berwald spaces), Tensor, N.S. 35 (1981), 25–39
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Bao, D., Chern, SS., Shen, Z. (2000). Berwald Spaces and Szabó’s Theorem for Berwald Surfaces. In: An Introduction to Riemann-Finsler Geometry. Graduate Texts in Mathematics, vol 200. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1268-3_10
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DOI: https://doi.org/10.1007/978-1-4612-1268-3_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7070-6
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