Displaying similar documents to “Jacobi Tensors and Ricci Curvature.”

On Jacobi fields and a canonical connection in sub-Riemannian geometry

Davide Barilari, Luca Rizzi (2017)

Archivum Mathematicum

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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.