论文标题
Sasakian歧管上的次曼尼亚人距离的变化以及耦合的应用
Variations of the sub-Riemannian distance on Sasakian manifolds with applications to coupling
论文作者
论文摘要
在Sasakian歧管及其自然存在的次曼尼亚式结构上，我们考虑沿着驯服的riemannian公制的大地测量学沿线图和镜像图。我们表明，这些运输图在亚riemannian切割局部外具有明确的限制。此类地图与任何连接有关的并行运输无关。我们使用此地图获得亚riemannian距离的第二个导数上的边界。作为应用程序，我们会在亚军棕色运动动作的耦合上获得一些初步结果。
On Sasakian manifolds with their naturally occurring sub-Riemannian structure, we consider parallel and mirror maps along geodesics of a taming Riemannian metric. We show that these transport maps have well-defined limits outside the sub-Riemannian cut-locus. Such maps are not related to parallel transport with respect to any connection. We use this map to obtain bounds on the second derivative of the sub-Riemannian distance. As an application, we get some preliminary result on couplings of sub-Riemannian Brownian motions.
