On Jacobi fields and canonical connection in sub-Riemannian geometry

Davide Barilari 1 Luca Rizzi 2, 3, 4
1 Géométrie et dynamique
IMJ - Institut de Mathématiques de Jussieu
4 GECO - Geometric Control Design
Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
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.
Complete list of metadatas

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01160902
Contributor : Luca Rizzi <>
Submitted on : Tuesday, March 28, 2017 - 12:13:23 PM
Last modification on : Wednesday, May 15, 2019 - 3:47:16 AM
Long-term archiving on : Thursday, June 29, 2017 - 4:47:39 PM

File

non-linear-connection.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

705

Files downloads

321