Hamenstädt, Ursula Some regularity theorems for Carnot-Caratheodory metrics. (English) Zbl 0687.53041 J. Differ. Geom. 32, No. 3, 819-850 (1990). The geodesics on a smooth manifold M with respect to a Carnot- Caratheodory metric induced by a smooth distribution Q and a smooth Riemannian metric on Q are investigated. At each point p of M an exponential map at p is defined which is of maximal rank on an open and dense subset of its domain of definition. It is shown that an isometry of the Carnot-Caratheodory metric is a smooth diffeomorphism of M. As an example, left invariant Carnot-Caratheodory metrics on nilpotent homogeneous Lie groups are studied. Reviewer: U.Hamenstädt Cited in 1 ReviewCited in 32 Documents MSC: 53C22 Geodesics in global differential geometry Keywords:geodesics; Carnot-Caratheodory metric; homogeneous Lie groups PDF BibTeX XML Cite \textit{U. Hamenstädt}, J. Differ. Geom. 32, No. 3, 819--850 (1990; Zbl 0687.53041) Full Text: DOI OpenURL