Title: Real hyperbolic hyperplane complements in the complex hyperbolic plane

Date: 12/08/2016

Time: 2:00 PM - 2:50 PM

Place: C304 Wells Hall

Speaker: Barry Minemyer, The Ohio State University

In the late 80's Gromov and Thurston constructed examples of manifolds which do not admit a hyperbolic metric but do admit metrics whose sectional curvature is pinched arbitrarily close to -1. Their construction involves taking cyclic branched covers of hyperbolic manifolds over 'nice' codimension two totally geodesic submanifolds. In a joint project with J.F. Lafont, J. Meyer, and B. Tshishiku we have extended this construction to 4-manifolds whose metric is modeled on the complex hyperbolic plane. This will be the content of the first half of the talk.
For this group project, I needed to understand the metric in the complex hyperbolic plane expressed in polar coordinates about a copy of the real hyperbolic plane. This research will make up the second half of the talk.