Geodesic
Singular pleated surfaces and CP1–structures
Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 179-190

Voir la notice de l'article provenant de la source Cambridge University Press

Let Fg be a closed orientable surface of genus g > 1 and let be the Teichmuller space of Fg, i.e., the space of marked hyperbolic structures on Fg We shall also denote by the space of marked hyperbolic structures on Fgwith one distinguished point; by this, we mean a distinguished point on the universal cover gof Fg. This space is isomorphic to the space of marked complete hyperbolic structures on a genus g surface with 1 cusp which is the usual interpretation of . Choose a decomposition of Fginto pairs of pants by a collection of non–intersecting, totally geodesic simple closed curves. The Fenchel–Nielsen coordinates for relative to this decomposition are given by the lengths of the curves as well as twist parameters defined on each curve. Varying the length and twist parameters gives deformations of the marked hyperbolic structures. 
Tan, Ser Peow. Singular pleated surfaces and CP1–structures. Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 179-190. doi: 10.1017/S0017089500031086
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