Engel Manifolds and Contact 3-Orbifolds
Engel Manifolds and Contact 3-Orbifolds
复制标题
Engel 歧管和 Contact 3-Orbifolds
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
K. Yamazaki
中科院分区：
文献类型：
--
作者：
K. Yamazaki
在早期的Engel流形研究中，R。蒙哥马利、嘉当延伸区和发展地图是中心人物。然而，只有在特有的叶理“漂亮”的情况下，才能对发展图进行全面界定。本文引入了切触3-orbifold的Cartan延拓和与更一般的Engel流形相联系的发展映射，并给出了Cartan延拓是流形的充要条件.此外，我们还解释了3维切触李群胚的Cartan延拓和与任何Engel流形相关联的发展映射，并证明了作为具有切触结构的“空间”的Cartan延拓的所有Engel流形都是由切触3-orbifold得到的.
In early study of Engel manifolds from R. Montgomery, the Cartan prolongation and the development map are central figures. However, the development map can be globally defined only if the characteristic foliation is "nice". In this paper, we introduce the Cartan prolongation of a contact 3-orbifold and the development map associated to a more general Engel manifold, and we give necessary and sufficient condition for the Cartan prolongation to be a manifold. Moreover, we explain the Cartan prolongation of a 3-dimensional contact \'etale Lie groupoid and the development map associated to any Engel manifold, and we proof that all Engel manifolds obtained as the Cartan prolongation of a "space" with contact structure are obtained from a contact 3-orbifold.