Liouville theorem, conformally invariant cones and umbilical surfaces for Grushin-type metrics
Differential Geometry
2010-04-13 v2 Metric Geometry
Abstract
We prove a classification theorem for conformal maps with respect to the control distance generated by a system of diagonal vector fields. It turns out that all such maps can be obtained as compositions of suitable dilations, inversions and isometries. We also classify all umbilical surfaces of the underlying metric.
Keywords
Cite
@article{arxiv.math/0607153,
title = {Liouville theorem, conformally invariant cones and umbilical surfaces for Grushin-type metrics},
author = {Daniele Morbidelli},
journal= {arXiv preprint arXiv:math/0607153},
year = {2010}
}
Comments
Revised version, to appear on Israel Journal of Mathematics. New title and added section 4 on umbilical surfaces