On 5-manifolds admitting rank two distributions of Cartan type
Differential Geometry
2019-07-08 v3 K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1603.09700,
title = {On 5-manifolds admitting rank two distributions of Cartan type},
author = {Shantanu Dave and Stefan Haller},
journal= {arXiv preprint arXiv:1603.09700},
year = {2019}
}
Comments
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)