Real Analytic Metrics on S^2 with Total Absence of Finite Blocking

Details Real Analytic Metrics on S^2 with Total Absence of Finite Blocking Real Analytic Metrics on S^2 with Total Absence of Finite Blocking

2011-09-07

arxiv.org/abs/1109.1336v1

Mathematics

Differential Geometry

30 pages, 5 figures

Scientific paper

If (M,g) is a Riemannian manifold and x,y are points in M, then a subset P of
M\{x,y} is said to be a blocking set for (x,y) if every geodesic from x to y
passes through a point of P. If no pair (x,y) in M X M has a finite blocking
set, then (M,g) is said to be totally insecure. We prove that there exist real
analytic metrics h on S^2 such that (S^2,h) is totally insecure.

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