Abstract
The Chern connection that we construct is a linear connection that acts on a distinguished vector bundle π*TM, sitting over the manifold TM \0 or SM. It is not a connection on the bundle TM over M. Nevertheless, it serves Finsler geometry in a manner that parallels what the Levi-Civita (Christoffel) connection does for Riemannian geometry. This connection is on equal footing with, but is different from, those due to Cartan, Berwald, and Hashiguchi (to name just a few).
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References
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Bao, D., Chern, SS., Shen, Z. (2000). The Chern Connection. 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_2
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DOI: https://doi.org/10.1007/978-1-4612-1268-3_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7070-6
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