A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space

Details A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space

2011-10-14

arxiv.org/abs/1110.3110v2

Mathematics

Differential Geometry

11 pages, no figure

Scientific paper

We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the Ahlfors islands theorem for it and the second one is to give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic three-space.

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