arXiv 0806.35722008-06-22math.DSmath.DG

Secure two-dimensional tori are flat

Victor Bangert, Eugene Gutkin

备注：: 15 pages, 4 figures

英文摘要：

A riemannian manifold is secure if the geodesics between any pair of points in the manifold can be blocked by a finite number of point obstacles. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. The conjecture claims, in particular, that a riemannian torus of any dimension is secure if and only if it is flat. We prove this for two-dimensional tori.

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