Complete flat cone metrics on punctured surfaces
Authors : Ismail Sağlam
Pages : 813-832
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.Keywords : Flat metric, the Gauss-Bonnet formula, surfaces with punctures, the Hopf-Rinow theorem