论文标题
在3D触点亚riemannian歧管的表面上的诱导几何形状上
On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds
论文作者
论文摘要
鉴于3D联系人次 - 里曼歧管$ m $中的表面$ s $，我们研究了长度空间的$ s $ $ s $ a $ s $的度量结构。首先，我们在特征点上定义了系数$ \ widehat k $，该点在当地确定了$ s $的特征性叶面。接下来，我们确定某些全球条件，使感应距离为有限。特别是，我们证明，诱导距离对于表面有限，该表面具有嵌入紧密的可协调分布的球体的拓扑结构，并具有孤立的特征点。
Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we investigate the metric structure induced on $S$ by $M$, in the sense of length spaces. First, we define a coefficient $\widehat K$ at characteristic points that determines locally the characteristic foliation of $S$. Next, we identify some global conditions for the induced distance to be finite. In particular, we prove that the induced distance is finite for surfaces with the topology of a sphere embedded in a tight coorientable distribution, with isolated characteristic points.
