On Jacobi fields and canonical connection in sub-Riemannian geometry

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.

13 pages, (v2) minor corrections. Final version to appear on Archivum Mathematicum

References in corpus (3)

• Sub-Riemannian curvature in contact geometry
• Comparison theorems for conjugate points in sub-Riemannian geometry
• Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds

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