论文标题
亚riemannian几何形状的仿射连接和曲率
Affine connections and curvature in sub-Riemannian geometry
论文作者
论文摘要
我们引入了一种新方法来计算亚里曼尼亚歧管的曲率。如Zelenko和Li所引入的，曲率在这里表示是大地测量学的雅各比曲线的符合性不变性。我们描述了如何使用兼容的仿射连接和诱导的张量来表达它们，而无需限制我们的亚riemannian歧管或连接的选择。特别是，我们获得了Riemannian类型的通用帽子定理。我们还为沿每个大地测量的规范水平框架提供了通用公式，并为计算曲率的算法提供了通用公式。包括几个示例以证明该理论。
We introduce a new approach for computing curvature of sub-Riemannian manifolds. Curvature is here meant as symplectic invariants of Jacobi curves of geodesics, as introduced by Zelenko and Li. We describe how they can be expressed using a compatible affine connection and induced tensors, without any restriction on our sub-Riemannian manifold or the choice of connection. In particular, we obtain a universal Bonnet-Myers theorem of Riemannian type. We also give universal formulas for the canonical horizontal frame along each geodesic and an algorithm for computing the curvature in general. Several examples are included to demonstrate the theory.
