标题： 接触几何中的正则性和乘积 显示英文标题

标题： The regularity and products in contact geometry

摘要： 我们研究了Reeb向量场完备的正则接触流形$(M,\eta)$，并证明它们是结构群为$S^1$或$\mathbb{R}$的典范主丛。 对于紧致的$M$，我们的证明非常简短且基础，并涵盖了著名的Boothby-Wang定理，但我们从一开始就不要求紧致性。 然而，为了在完全一般的情况下证明我们的结果，我们使用了一些适用于光滑纤维丛的拓扑工具。 在论文的第二部分中，我们描述了普遍接触流形的接触积的一个自然概念，以及主接触流形的积，当Reeb向量场的周期是共度时，这种积存在，并对应于辛流形的预量子化丛的积构造。 显示英文摘要

摘要： We study regular contact manifolds $(M,\eta)$ whose Reeb vector field is complete and prove that they are canonically principal bundles with the structure group $S^1$ or $\mathbb{R}$. For compact $M$, our proof is very short and elementary and covers the celebrated Boothby-Wang theorem, but we do not assume compactness from the very beginning. However, to prove our result in full generality we use some topological tools adapted to smooth fibrations. In the second part of the paper, we describe a natural concept of contact products of general contact manifolds as well as a product of principal contact manifolds, which exists if the periods of the Reeb vector fields are commensurate, and corresponds to the construction of products of prequantization bundles of symplectic manifolds.