Geodesic
On Jacobi fields and a canonical connection in sub-Riemannian geometry
Archivum mathematicum, Tome 53 (2017) no. 2, pp. 77-92

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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 [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.
DOI : 10.5817/AM2017-2-77
Classification : 53B15, 53B21, 53C17
Keywords: sub-Riemannian geometry; curvature; connection; Jacobi fields 
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Barilari, Davide; Rizzi, Luca. On Jacobi fields and a canonical connection in sub-Riemannian geometry. Archivum mathematicum, Tome 53 (2017) no. 2, pp. 77-92. doi: 10.5817/AM2017-2-77

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