  We introduce a new approach for computing curvature of sub-Riemannian
manifolds. Curvature is here meant as symplectic invariants of Jacobi curves of
geodesics, as introduced by Zelenko and Li. We describe how they can be
expressed using a compatible affine connection and induced tensors, without any
restriction on our sub-Riemannian manifold or the choice of connection. In
particular, we obtain a universal Bonnet-Myers theorem of Riemannian type. We
also give universal formulas for the canonical horizontal frame along each
geodesic and an algorithm for computing the curvature in general. Several
examples are included to demonstrate the theory.

Differential Geometry