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Isometries of Carnot groups and sub-Finsler homogeneous manifolds. (English) Zbl 1343.53029
The paper deals with a fundamental problem in geometry which consists of the study of spaces that are isometrically homogeneous, i.e., metric spaces on which the group of isometries acts transitively. The authors prove that isometries between open sets of Carnot groups are affine and each isometry of a sub-Riemannian manifold is determined by the horizontally differential at one point. Also, they extend the result to sub-Finslerian homogeneous manifolds and study the regularity of isometries of homogeneous manifolds equipped with homogeneous distances that induce the topology of manifold.

MSC:
53C17 Sub-Riemannian geometry
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
22F50 Groups as automorphisms of other structures
53C30 Differential geometry of homogeneous manifolds
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