Existence and uniqueness of Chern connection in the Klein-Grifone approach

2014/02/03 by Nabil L. Youssef, Youssef, Nabil L., S. G. Elgendi +1 · 1 citation
Mathematics · Physics and Astronomy · #53B40 #53C12 #53C60 #58B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53B40 #msc:53C12 #msc:53C60 #msc:58B20

paper · pdf · doi:10.48550/arxiv.1402.0317

LaTeX file, 14 pages

arxiv created 2014/02/03 · openalex publication_date 2014/02/03 · arxiv updated 2014/02/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Klein-Grifone approach to global Finsler geometry is adopted. A global existence and uniqueness theorem for Chern connection is formulated and proved. The torsion and curvature tensors of Chern connection are derived. Some properties and the Bianchi identities for this connection are investigated. A concise comparison between Berwald, Cartan and Chern connections is presented.

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