Abstract
It was L. Berwald [Bw1] who first introduced the notion of connection for Finsler metrics. After his remarkable work, several connections were introduced from various approaches. The well-known connections are the Cartan connection [Ca] and the Chern connection [Ch1] [BaCh]. They all differ from the Berwald connection by the Cartan torsion, or the Landsberg curvature, or their linear combination. But only the Berwald connection can be extended to sprays! Therefore, we will mainly discuss the Berwald connection throughout this book. One is referred to [BaChSh1][Ma4][Sh1] for other connections.
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© 2001 Springer Science+Business Media Dordrecht
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Shen, Z. (2001). Connections. In: Differential Geometry of Spray and Finsler Spaces. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9727-2_8
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DOI: https://doi.org/10.1007/978-94-015-9727-2_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5673-3
Online ISBN: 978-94-015-9727-2
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