On the classification of singular flat structures on surfaces

Ousama Malouf (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an answer to this question in the case of flat structures on pairs of pants with one singular point. The question of decomposability of an arbitrary flat surface into flat pairs of pants is discussed.

Mots clés: Flat structure; Teichmüller space; conical singularity

Domaines: Géométrie métrique [math.MG]

Ousama Malouf. On the classification of singular flat structures on surfaces. Balkan Journal of Geometry and Its Applications, 2010, 15 (1), pp.90-103. ⟨hal-00442654⟩