论文标题
在紧凑的对称空间上计算测量学
Counting geodesics on compact symmetric spaces
论文作者
论文摘要
我们将紧凑型对称空间的底座上的riemannian指数图的逆图描述为通过最大圆环所谓的焦点轨道的不相交联合。这些是作用在底线切线空间中的各向同性组的子组的轨道。我们展示了它们的尺寸（无限数据）和连接的组件（拓扑数据）是在对称空间的图，多重性，Weyl组和晶格中编码的。获取这些数据正是我们通过计算测量学的含义。这扩展了紧凑型谎言组的先前结果。我们应用结果，为紧凑的对称空间提供了简短的独立证明。
We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting in the tangent space at the basepoint. We show how their dimensions (infinitesimal data) and connected components (topological data) are encoded in the diagram, multiplicities, Weyl group and lattice of the symmetric space. Obtaining this data is precisely what we mean by counting geodesics. This extends previous results on compact Lie groups. We apply our results to give short independent proofs of known results on compact symmetric spaces.
