论文标题
$ h $ - 原理，用于嵌入到接触结构的横向
An $h$-principle for embeddings transverse to a contact structure
论文作者
论文摘要
给定一类嵌入到触点或符号歧管中的嵌入，我们给出了足够的条件，即我们称之为同性恋或等值连接实现，以使该类满足一般的$ h $ - 原理。灵活性是从$ h $ - 原始的等距和等距嵌入式嵌入，它为经典结果提供了一个框架，我们提供了两个新的应用程序。我们的主要结果是，横向到接触结构的嵌入在两种情况下满足完整的$ h $原理：如果嵌入的补体被隔开，或者当形式导数的图像与接触结构的相交相交的相互作用严格包含在适当的Symplectic Subbundle中。我们通过通过一类嵌入在常规水平集上研究哈密顿动力学的普遍性来说明符号流形的一般框架。
Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general $h$-principle. The flexibility follows from the $h$-principles for isocontact and isosymplectic embeddings, it provides a framework for classical results, and we give two new applications. Our main result is that embeddings transverse to a contact structure satisfy a full $h$-principle in two cases: if the complement of the embedding is overtwisted, or when the intersection of the image of the formal derivative with the contact structure is strictly contained in a proper symplectic subbundle. We illustrate the general framework on symplectic manifolds by studying the universality of Hamiltonian dynamics on regular level sets via a class of embeddings.
