期刊
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
卷 239, 期 -, 页码 -出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2023.113421
关键词
Sub -Riemannian geometry; Conjugate points; Metric geometry
This article proves that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points, and characterizes conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space.
We prove that the sub-Riemannian exponential map is not injective in any neighbourhood of certain critical points. Namely that it does not behave like the injective map of reals given by f(x) = x3 near its critical point x = 0. As a consequence, we characterise conjugate points in ideal sub-Riemannian manifolds in terms of the metric structure of the space. The proof uses the Hilbert invariant integral of the associated variational problem. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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