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Regularity and Continuity properties of the sub-Riemannian exponential map

Borza, Samuël; Klingenberg, Wilhelm

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Authors

Samuël Borza



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.

Citation

Borza, S., & Klingenberg, W. (2023). Regularity and Continuity properties of the sub-Riemannian exponential map. Journal of Dynamical and Control Systems, 29(4), 1385-1407. https://doi.org/10.1007/s10883-022-09624-y

Journal Article Type Article
Acceptance Date Oct 30, 2022
Online Publication Date Jan 26, 2023
Publication Date Oct 1, 2023
Deposit Date Sep 28, 2022
Publicly Available Date Apr 20, 2023
Journal Journal of Dynamical and Control Systems
Print ISSN 1079-2724
Electronic ISSN 1573-8698
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 29
Issue 4
Pages 1385-1407
DOI https://doi.org/10.1007/s10883-022-09624-y
Keywords Conjugate points, 53B15, Metric geometry, 49J15, Sub-Riemannian geometry, 53B99, 53C17
Public URL https://durham-repository.worktribe.com/output/1190468

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Advance online version This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.






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