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Geometric objects associated with the fundamental connections in Finsler geometry

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arxiv 0805.2489 v2 pith:IE4IX5YS submitted 2008-05-16 math.DG gr-qcmath-phmath.MP

classification math.DGgr-qcmath-phmath.MP
keywords associatedconnectionfinslerconnectionsfundamentalgeometricobjectsgeometry
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The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the most general relations concerning the torsion tensor fields and the curvature tensor fields associated with a given regular connection on the pullback bundle of a Finsler manifold. These relations, in turn, play a key role in obtaining other interesting results concerning the properties of the most important geometric objects associated with the fundamental canonical linear connections on the pullback bundle of a Finsler manifold, namely, the Cartan connection, the Berwald connection, the Chern (Rund) connection and the Hashiguchi connection. For the sake of completeness and for comparison reasons, we provide an appendix presenting a global survey of canonical linear connections in Finsler geometry and the fundamental geometric objects associated with them.

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  1. On Generalized Matsumoto Metrics with a Special $\pi$-form

    math.DG 2025-10 conditional novelty 5.0 of 10

    For a Finsler metric with a concurrent π-vector field, bF = F^2/(F - Φ) is a conic Finsler structure exactly when F(1 + 2g(φ,φ)) - 3Φ ≠ 0, with explicit global transformation formulas for the associated geometric objects.

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