2000 | OriginalPaper | Buchkapitel
The Chern Connection
verfasst von : D. Bao, S.-S. Chern, Z. Shen
Erschienen in: An Introduction to Riemann-Finsler Geometry
Verlag: Springer New York
Enthalten in: Professional Book Archive
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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).