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On Jacobi fields and canonical connection in sub-Riemannian geometry (1506.01827v3)
Published 5 Jun 2015 in math.DG, math.MG, and math.OC
Abstract: In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [Zelenko-Li]. We show why this connection is naturally nonlinear, and we discuss some of its properties.
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