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.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1439-1454
Launched on MUSE
2016-09-27
Open Access
No
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