论文标题
曲率和等效性问题
Curvature and the equivalence problem in sub-Riemannian geometry
论文作者
论文摘要
这些注释介绍了亚里曼尼亚歧管的等效问题。我们首先在连接，框架束和亚曼尼曼几何形状方面引入初步。然后，我们达到了这些音符的主要目的，即给出具有恒定符号的子里曼歧管上存在的规范分级和连接的描述。这些结构正是确定两个歧管是否是等距的所需的。我们提供了三个具体示例，即恩格尔（2,3,4） - 曼佛，触点歧管和cartan（2,3,5） - manifolds。 这些笔记是\ href {https://conference.math.muni.cz/srni/} {42nd Winter School：几何和物理学}，Snrí，Snrí，Check Republic，大多数基于其他早期的工作。但是，关于恩格尔（2,3,4） - manifolds的工作是原始的研究，并说明了重要的特殊情况是我们的模型具有最小的同量。
These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which are Engel (2,3,4)-manifolds, contact manifolds and Cartan (2,3,5)-manifolds. These notes are an edited version of a lecture series given at the \href{https://conference.math.muni.cz/srni/}{42nd Winter school: Geometry and Physics}, Snrí, Check Republic, mostly based on other earlier work. However, the work on Engel (2,3,4)-manifolds is original research, and illustrate the important special case were our model has the minimal set of isometries.
