On the classification of singular flat structures on surfaces

Details On the classification of singular flat structures on surfaces On the classification of singular flat structures on surfaces

2009-12-22

arxiv.org/abs/0912.4483v1

Balkan Journal of Geometry and Its Applications 15, 1 (2010) 90-103

Mathematics

Metric Geometry

Thirteen pages, prepublication

Scientific paper

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.

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