不具有有限块性质的黎曼度量的稠密G-δ集
A dense G-delta set of Riemannian metrics without the finite blocking property
摘要：
称黎曼流形（M，g）中的一对点（x，y）具有有限阻塞性质，如果存在包含在M\{x，y}中的有限集P，使得从x到y的每一测地线段都通过P中的一点.我们证明了对任意至少为2维的闭C-无穷流形M和M x M中的每一对（x，y），存在M上的C-无穷黎曼度量的稠密G-δ集，使得（x，y）对于该集中的每个g都不具有有限阻塞性质。
英文摘要：
A pair of points (x,y) in a Riemannian manifold (M,g) is said to have the finite blocking property if there is a finite set P contained in M\{x,y} such that every geodesic segment from x to y passes through a point of P. We show that for every closed C-infinity manifold M of dimension at least two and every pair (x,y) in M x M, there exists a dense G-delta set of C-infinity Riemannian metrics on M such that (x,y) fails to have the finite blocking property for every g in that set.
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