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.
On Jacobi fields and a canonical connection in sub-Riemannian geometry / Barilari, D.; Rizzi, L.. - In: ARCHIVUM MATHEMATICUM. - ISSN 0044-8753. - 53:(2017), pp. 77-92. [10.5817/AM2017-2-77]
On Jacobi fields and a canonical connection in sub-Riemannian geometry
Rizzi, L.
2017-01-01
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 [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.File in questo prodotto:
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