Total curvature of complete surfaces in hyperbolic space

Details Total curvature of complete surfaces in hyperbolic space Total curvature of complete surfaces in hyperbolic space

2009-02-04

arxiv.org/abs/0902.0672v2

Advances in Mathematics 225 (2010), no. 2, 805-825

Mathematics

Differential Geometry

Scientific paper

10.1016/j.aim.2010.03.015

We prove a Gauss-Bonnet formula for the extrinsic curvature of complete
surfaces in hyperbolic space under some assumptions on the asymptotic
behaviour. The result is given in terms of the measure of geodesics
intersecting the surface non-trivially, and of a conformal invariant of the
curve at infinity.

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