Communications in Analysis and Geometry

Volume 20 (2012)

Number 4

Parabolic (3, 5, 6)-distributions and GL(2)-structures

Pages: 781 – 802

DOI: http://dx.doi.org/10.4310/CAG.2012.v20.n4.a4

Author

Wojciech Kryński (Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland)

Abstract

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.

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