On 5-manifolds admitting rank two distributions of Cartan type

TL;DR

This paper investigates the conditions under which 5-manifolds can admit rank two distributions of Cartan type, providing complete solutions for open manifolds and partial results for closed manifolds, including topological classifications and new examples.

Contribution

It offers a complete topological classification for open 5-manifolds and partial geometric results for closed 5-manifolds regarding Cartan type distributions.

Findings

Complete classification for open manifolds.

Topological constraints for closed manifolds.

New examples of 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.