Insecurity for compact surfaces of positive genus |
| |
Authors: | Victor Bangert Eugene Gutkin |
| |
Institution: | 1.Mathematisches Institut,Albert-Ludwigs-Universit?t,Freiburg im Breisgau,Germany;2.Nicolaus Copernicus University (UMK), and Mathematics Institute of the Polish Academy of Sciences (IMPAN),Torun,Poland |
| |
Abstract: | A pair of points in a riemannian manifold M is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of
points is insecure. A manifold is secure if all pairs of points in M are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure.
Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds.
We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with
any riemannian metric and a closed surface of genus one with generic metric are totally insecure. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|