Smoothness of subRiemannian isometries
Metric Geometry
2014-02-26 v2 Analysis of PDEs
Differential Geometry
Abstract
We show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.
Keywords
Cite
@article{arxiv.1305.5286,
title = {Smoothness of subRiemannian isometries},
author = {Luca Capogna and Enrico Le Donne},
journal= {arXiv preprint arXiv:1305.5286},
year = {2014}
}
Comments
14 pages, reflecting feedback from several readers. New result: Corollary 1.8