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On the geometry of flat surfaces with a single singularity

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Abstract

If T is a flat torus with boundary and a conical singularity in its boundary then the isometry type of T is determined by the lengths of five closed geodesics. As a corollary the isometry type of a flat closed surface S with a single conical singularity is determined by the lengths of finitely many closed geodesics provided that S admits a special decomposition.

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Authors and Affiliations

  1. Agricultural University Athens, Athens, Greece

    Charalampos Charitos & Ioannis Papadoperakis

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  1. Charalampos Charitos
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  2. Ioannis Papadoperakis
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Correspondence to Charalampos Charitos.

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Charitos, C., Papadoperakis, I. On the geometry of flat surfaces with a single singularity. J. Geom. 106, 255–278 (2015). https://doi.org/10.1007/s00022-014-0246-y

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  • DOI: https://doi.org/10.1007/s00022-014-0246-y

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