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Regularity and Continuity properties of the sub-Riemannian exponential map

Borza, Samuël and Klingenberg, Wilhelm (2022) 'Regularity and Continuity properties of the sub-Riemannian exponential map.', Journal of Dynamical and Control Systems .

Abstract

We prove a version of Warner's regularity and continuity properties for the sub-Riemannian exponential map. The regularity property is established by considering sub-Riemannian Jacobi fields while the continuity property follows from studying the Maslov index of Jacobi curves. We finally show how this implies that the exponential map of the three dimensional Heisenberg group is not injective in any neighbourhood of a conjugate vector.

Item Type:Article
Full text:Publisher-imposed embargo
(AM) Accepted Manuscript
File format - PDF
(464Kb)
Status:Peer-reviewed
Publisher Web site:https://www.springer.com/journal/10883
Date accepted:No date available
Date deposited:28 September 2022
Date of first online publication:No date available
Date first made open access:No date available

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