Calculus of Variations and Geometric Measure Theory

D. Barilari - L. Rizzi

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

created by rizzi1 on 04 Jun 2015
modified on 05 Jul 2017


Published Paper

Inserted: 4 jun 2015
Last Updated: 5 jul 2017

Journal: Archivum Mathematicum
Volume: 53
Number: 2
Pages: 77-92
Year: 2017
Doi: 10.5817/AM2017-2-77

ArXiv: 1506.01827 PDF


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