关于容许Cartan型秩二分布的五维流形
微分几何
2019-07-08 v3 K理论与同调
摘要
我们考虑一个可定向五维流形能否配备Cartan型秩二分布，以及哪些2平面丛可以实现的问题。我们对开流形得到了完整答案。在闭流形情形，我们解决了该问题的拓扑部分，并给出了关于其几何方面的部分结果以及新例子。
引用
@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}
}
备注
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)