On the remarkable properties of the hyperbolic Whitehead link cone-manifold

Denote by W(m, n) the hyperbolic cone-manifold whose underlying space is the 3-sphere and singular geodesics are formed by two components of the Whitehead link with cone angles 2π/m and 2π/n. The aim of the paper is to establish the Tangent and Sine Rules relating the complex lengthes of the singular geodesics and the cone angles of W(m, n). An explicit upper bound for the real length of the singular geodesic is also given.