Integrability Conditions for the Grushin and Martinet Distributions
by Ovidiu Calin   Der-Chen Chang  

Vol. 8 No. 2 (2013) P.159~P.168

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
Grushin, Martinet, Integrability conditions, Differential complexes

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 58J10,37J30

MILESTONES

Received: 2012-08-10
Revised : 2013-01-19
Accepted: 2013-01-20

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