Constructing Complete Projectively Flat Connections
نویسنده
چکیده
Theorem 1. Let T 2 be the two dimensional torus. Then for any positive integer m there is a complete torsion free projectively flat connection, ∇, on T 2 such that for any point p ∈ T 2 there is a point q ∈ T 2 with the property that any broken ∇-geodesic between p and q has at least m breaks. Moreover if T 2 is viewed as a Lie group in the usual manner, this connection is invariant under translations by elements of T .
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