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arXiv · 0806.3572

Secure two-dimensional tori are flat

Victor Bangert·Eugene Gutkin
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Abstract

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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Victor Bangert, Eugene Gutkin. 2008-06-22. Secure two-dimensional tori are flat. https://arxiv.org/abs/0806.3572

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