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Keywords:
sub-Riemannian geometry; curvature; connection; Jacobi fields
sub-Riemannian geometry; curvature; connection; Jacobi fields
Summary:
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.
References:
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