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Geodesics and isometries of Carnot groups. (English) Zbl 1060.53039
The author proves that an isometry of a two-step Carnot group which fixes the identity is an automorphism of the nilpotent Lie group and derives from previously known results that the same holds for all Carnot groups, i.e. nilpotent Lie groups with left-invariant sub-Riemannian metrics.

MSC:
53C17 Sub-Riemannian geometry
57S25 Groups acting on specific manifolds
53C22 Geodesics in global differential geometry
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