Communications in Analysis and Geometry
Volume 20 (2012)
Parabolic (3, 5, 6)-distributions and GL(2)-structures
Pages: 781 – 802
We consider rank-three distributions with growth vector (3, 5, 6). The class of such distributions splits into three subclasses: parabolic, hyperbolic and elliptic. In the present paper, we deal with the parabolic case. We provide a classification of such distributions and exhibit connections between them and GL(2)-structures. We prove that any GL(2)-structure on three- and four-dimensional manifold can be described as a parabolic (3, 5, 6)-distribution.