A remark on spaces of flat metrics with cone singularities of constant sign curvatures
A remark on spaces of flat metrics with cone singularities of constant sign curvatures
By a result of W. P. Thurston, the moduli space of flat metrics on the sphere with n cone singularities of prescribed positive curvatures is a complex hyperbolic orbifold of dimension n-3. The Hermitian form comes from the area of the metric. Using geometry of Euclidean polyhedra, we observe that …