Calculus of Variations and Geometric Measure Theory
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E. Le Donne - A. Ottazzi

Isometries of Carnot groups and subFinsler homogeneous manifolds

created by ledonne on 21 Dec 2018

[BibTeX]

preprint

Inserted: 21 dec 2018

Year: 2012

ArXiv: 1210.5097 PDF

Abstract:

We show that isometries between open sets of Carnot groups are affine. This result generalizes a result of Hamenstadt. Our proof does not rely on her proof. In addition, we study global isometries of general homogeneous manifolds equipped with left-invariant subFinsler distances. We show that each isometry is determined by the blow up at one point. For proving the results, we consider the action of isometries on the space of Killing vector fields. We make use of results by Capogna-Cowling and by Gleason-Montgomery-Zippin for obtaining smoothness of the isometric action.

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