Fat分布中水平浸入的存在性
Existence of Horizontal Immersions in Fat Distributions
AI总结：
本文为余秩2的fat分布定义了数值不变量“度”，并利用Gromov的h-原理技术证明了任意流形到度为2的fat分布及四元数接触结构中水平浸入的存在性。
摘要：
接触结构及其全纯和四元数对应物是强括号生成（或fat）分布的主要示例。本文为流形上的余秩2 fat分布关联了一个数值不变量，称为分布的度。全纯接触结构底层的实分布的度为2。利用Gromov的h-原理的层理论与解析技术，我们证明了任意流形到度为2的fat分布和四元数接触结构中的水平浸入的存在性。我们还研究了诱导给定接触结构的接触流形的浸入。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
