On the remarkable properties of the hyperbolic Whitehead link cone-manifold (Q2725553)

Recall that a 3-dimensional hyperbolic cone-manifold is a 3-dimensional Riemannian manifold of constant negative sectional curvature with cone-type singularities along simple closed geodesics. Denote by \(W(m,n)\) a hyperbolic cone-manifold whose underlying space is the 3-sphere and whose singular geodesics are formed by two components of the Whitehead link with cone angles \(2\pi/m\) and \(2\pi/n\). The aim of the paper under review is to establish the Tangent and Sine Rules relating the complex lengths of the singular geodesics and the cone angles of \(W(m,n)\). An explicit upper bound for the real length of the singular geodesics is also given.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00034].