Calculus of Variations and Geometric Measure Theory
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D. Barilari - L. Rizzi

On Jacobi fields and canonical connection in sub-Riemannian geometry

created by rizzi1 on 04 Jun 2015
modified on 15 May 2017


Accepted Paper

Inserted: 4 jun 2015
Last Updated: 15 may 2017

Journal: Archivum Mathematicum
Pages: 13
Year: 2015

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


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