Inserted: 12 mar 2009
Last Updated: 10 jan 2012
Journal: Proc. Amer. Math. Soc.
Involutivity is a well known necessary condition for integrability of smooth tangent distributions. We show that this condition is still necessary for integrability with Sobolev surfaces. We specialize our study to the left invariant horizontal distribution of the first Heisenberg group. Here we answer a question raised in a paper by Z.M.Balogh, R.Hoefer-Isenegger, J.T.Tyson.