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On Jacobi fields and canonical connection in sub-Riemannian geometry

Davide Barilari 1 Luca Rizzi 2, 3, 4
1 Géométrie et dynamique [Paris]
IMJ - Institut de Mathématiques de Jussieu
4 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
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.
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Submitted on : Tuesday, March 28, 2017 - 12:13:23 PM
Last modification on : Saturday, June 19, 2021 - 3:50:31 AM
Long-term archiving on: : Thursday, June 29, 2017 - 4:47:39 PM

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Davide Barilari, Luca Rizzi. On Jacobi fields and canonical connection in sub-Riemannian geometry. Archivum Mathematicum, Masarykova Universita, 2017, 53 (2), pp.77-92. ⟨10.5817/AM2017-2-77⟩. ⟨hal-01160902v2⟩

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