论文标题
Euler样矢量场，正常形式和各向同性嵌入
Euler-like vector fields, normal forms, and isotropic embeddings
论文作者
论文摘要
歧管的子曼膜n的管状邻域嵌入的细菌与M附近的Euler样矢量场的细菌属于一对一的对应关系。在许多情况下，这会降低与给定结构构造的几何结构的“正常形式结果”的证明。我们在各种示例中说明了这一原理，包括莫尔斯·鲍特·莱姆玛（Morse-Bott Lemma），温斯坦（Weinstein）的拉格朗日（Weinstein）嵌入定理以及Zung的线性化定理，用于适当的lide lie gropsoids。在本文的第二部分中，我们将理论扩展到了加权上下文，并应用了各向同性嵌入。
Germs of tubular neighborhood embeddings for submanifolds N of manifolds M are in one-one correspondence with germs of Euler-like vector fields near N. In many contexts, this reduces the proof of `normal forms results' for geometric structures to the construction of an Euler-like vector field compatible with the given structure. We illustrate this principle in a variety of examples, including the Morse-Bott lemma, Weinstein's Lagrangian embedding theorem, and Zung's linearization theorem for proper Lie groupoids. In the second part of this article, we extend the theory to a weighted context, with an application to isotropic embeddings.
