Angle structures and hyperbolic $3$-manifolds with totally geodesic boundary

Faze Zhang, Ruifeng Qiu, Tian Yang

Published 2014-05-07, updated 2014-05-11Version 2

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and conversely each hyperbolic $3$-manifold with totally geodesic boundary has an ideal triangulation that admits angle structures.