CAT(1) metrics on spheres
by
Gábor Moussong
The Ohio State University

The observation that any spacelike convex hypersurface in the (n+1)-dimensional Minkowski space carries a natural CAT(0) metric leads to the proof that for any convex body in hyperbolic n-space the natural metric on the space of supporting hyperplanes is a CAT(1) metric on the (n-1)-sphere with the additional property that each closed geodesic is strictly longer than 2pi. For n=3, as an extension of Rivin's characterization of hyperbolic convex polyhedra, we find that such metrics on the 2-sphere are in bijective correspondence with convex bodies in hyperbolic 3-space.

Date received: May 6, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cabb-42.