论文标题
部分可观测时空混沌系统的无模型预测
A sub-Riemannian Gauss-Bonnet theorem for surfaces in contact manifolds
论文作者
论文摘要
我们获得了经典的高斯河内定理的次摩nanian版本。我们考虑了三维接触次摩曼尼亚歧管的子表面，并使用驯服的riemannian度量的家族，在极限中获得了纯的亚里曼尼亚式结果。特别是，我们能够从特征集周围的几何形状（即，在表面上的切线空间和接触结构重合的点）中恢复表面的拓扑信息。我们都为没有边界的表面和边界表面提供了一个版本。
We obtain a sub-Riemannian version of the classical Gauss-Bonnet theorem. We consider subsurfaces of a three dimensional contact sub-Riemannian manifolds, and using a family of taming Riemannian metric, we obtain a pure sub-Riemannian result in the limit. In particular, we are able to recover topological information of the surface from the geometry around the characteristic set, i.e., the points where the tangent space to the surface and contact structure coincide. We both give a version for surfaces without boundary and surfaces with boundary.
