2008/01/18 by M. I. Wanas, M. I. WANAS · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Mathematics and Applications #gr-qc #math.DG
paper · pdf · doi:10.1142/s0217732309030412
published as Mod.Phys.Lett.A24:1749-1762,2009 · 13 pages, LaTeX file, typographical corrections. Part of a talk presented at The International Conference on "Finsler Extensions of Relativity Theory" held at Cairo, Egypt, November 4-10,2006
arxiv created 2008/01/18 · openalex publication_date 2009/07/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structure are assumed to be functions of position and direction. A nonlinear connection emerges naturally and is defined in terms of the building blocks of the structure. Two linear connections, one of Berwald type and the other of the Cartan type, are defined using the nonlinear connection of the FAP. Both linear connections are nonsymmetric and consequently admit torsion. A metric tensor is defined in terms of the building blocks of the structure. The condition for this metric to be a Finslerian one is obtained. Also, the condition for an FAP-space to be an AP-one is given.