论文标题
水平浸入脂肪分布中
Existence of Horizontal Immersions in Fat Distributions
论文作者
论文摘要
接触结构及其全体形态和Quaternionic对应物是强烈括号产生（或脂肪）分布的主要例子。在本文中，我们将数值不变性与Corank $ 2 $ fat分布相关联，称为分布的\ emph {gemph {gemph}。全体形态接触结构的实际分布为$ 2 $。使用Gromov的捆绑理论和分析技术，我们证明了任意歧管中的水平沉浸式存在于$ 2 $ 2 $脂肪分布和Quaternionic接触结构中。我们还研究了诱导给定接触结构的接触歧管的浸入。
Contact structures, as well as their holomorphic and quaternionic counterparts are the primary examples of strongly bracket generating (or fat) distributions. In this article we associate a numerical invariant to corank $2$ fat distribution on manifolds, referred to as \emph{degree} of the distribution. The real distribution underlying a holomorphic contact structure is of degree $2$. Using Gromov's sheaf theoretic and analytic techniques of $h$-principle, we prove the existence of horizontal immersions of an arbitrary manifold into degree $2$ fat distributions and the quaternionic contact structures. We also study immersions of a contact manifold inducing the given contact structure.
