Integrability conditions for the Grushin and Martinet distributions
Differential Geometry
2012-07-24 v1
Abstract
We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive the integrability conditions for the Grushin and Martinet distributions and build certain complexes of differential operators. These complexes are well-behaved despite the distributions they resolve being non-regular.
Keywords
Cite
@article{arxiv.1207.5440,
title = {Integrability conditions for the Grushin and Martinet distributions},
author = {Ovidiu Calin and Der-Chen Chang and Michael Eastwood},
journal= {arXiv preprint arXiv:1207.5440},
year = {2012}
}
Comments
8 pages