On Jacobi fields and a canonical connection in sub-Riemannian geometry
Copyright policy )On Jacobi fields and a canonical connection in sub-Riemannian geometry
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.
13 pages, (v2) minor corrections. Final version to appear on Archivum Mathematicum
- Grenoble Alpes University France
- University of Padua Italy
- Sorbonne University France
- Sorbonne Université France
- Joseph Fourier University France
Mathematics - Differential Geometry, 53C17, 53B21, 53B15, MSC: 53C17, 53B21, Other connections, 510, Mathematics - Metric Geometry, Connection, FOS: Mathematics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Mathematics - Optimization and Control, Connection; Curvature; Jacobi fields; Sub-Riemannian geometry, Curvature, Methods of local Riemannian geometry, connection, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Metric Geometry (math.MG), 53B15, Sub-Riemannian geometry, sub-Riemannian geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Jacobi fields, Optimization and Control (math.OC), curvature, Jacobi fi elds, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
Mathematics - Differential Geometry, 53C17, 53B21, 53B15, MSC: 53C17, 53B21, Other connections, 510, Mathematics - Metric Geometry, Connection, FOS: Mathematics, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Mathematics - Optimization and Control, Connection; Curvature; Jacobi fields; Sub-Riemannian geometry, Curvature, Methods of local Riemannian geometry, connection, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], Metric Geometry (math.MG), 53B15, Sub-Riemannian geometry, sub-Riemannian geometry, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Jacobi fields, Optimization and Control (math.OC), curvature, Jacobi fi elds, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
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