Abstract
Let (M, F) be a Finsler manifold, where F is C∞ on TM \0 and is positively (but perhaps not absolutely) homogeneous of degree 1. Fix T ∈ T p M. Consider the constant speed geodesic σ(t) = exp p (tT), 0 ⩽ t ⩽ r that emanates from p = σ(0) and terminates at q = σ(r). If there is no confusion, label its velocity field by T also. Let D T denote covariant differentiation along σ, with reference vector T. This concept was introduced in the Exercise portion of 5.2.
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Bao, D., Chern, SS., Shen, Z. (2000). The Index Form and the Bonnet—Myers Theorem. 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_7
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DOI: https://doi.org/10.1007/978-1-4612-1268-3_7
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