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.

DOI

10.3906/mat-1806-23

Keywords

Flat metric, the Gauss-Bonnet formula, surfaces with punctures, the Hopf-Rinow theorem

First Page

813

Last Page

832

Recommended Citation

SAĞLAM, İ (2019). Complete flat cone metrics on punctured surfaces. Turkish Journal of Mathematics 43 (2): 813-832. https://doi.org/10.3906/mat-1806-23

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