Regularity and Continuity properties of the sub-Riemannian exponential map - Borza, Samuël; Klingenberg, Wilhelm (Journal of Dynamical and Control Systems, 2023)
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.
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Keywords: Conjugate points; 53B15; Metric geometry; 49J15; Sub-Riemannian geometry; 53B99; 53C17