Inserted: 4 jun 2015
Last Updated: 5 jul 2017
Journal: Archivum Mathematicum
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.
Keywords: Curvature, sub-Riemannian, connection, Jacobi fields