On 5-manifolds admitting rank two distributions of Cartan type

Abstract

We consider the question whether an orientable 5-manifold can be equipped with a rank two distribution of Cartan type and what 2-plane bundles can be realized. We obtain a complete answer for open manifolds. In the closed case, we settle the topological part of this problem and present partial results concerning its geometric aspects and new examples.

v3: accepted manuscript, added journal reference, DOI, and secondary MSC classification. v2: results unchanged; no substantial changes; minor modifications (typos; additional references; a paragraph on existence of Engel structures in the introduction; a remark on the simply connected case below Theorem 1; more comments at the beginning of Section 4)

References in corpus (3)

• The twistor spinors of generic 2- and 3-distributions
• On Nurowski's conformal structure associated to a generic rank two distribution in dimension five
• On automorphism groups of some types of generic distributions

Cited by in corpus (5)

• Graded hypoellipticity of BGG sequences
• The heat asymptotics on filtered manifolds
• Analytic torsion of generic rank two distributions in dimension five
• Analytic torsion of nilmanifolds with (2,3,5) distributions
• Regularized determinants of the Rumin complex in irreducible unitary representations of the (2,3,5) nilpotent Lie group