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Flat fronts in hyperbolic 3-space with prescribed singularities

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Abstract

The paper deals with the study of flat fronts in the hyperbolic 3-space, \(\mathbb {H}^3\). We characterize when an analytic curve of \(\mathbb {H}^3\) is in the singular set of some flat front with prescribed cuspidal edges and swallowtail singularities. We also prove that every complete flat front with a non-degenerate analytic planar singular set must be rotational.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Universidad de Granada, 18071 , Granada, Spain

    Antonio Martínez & Francisco Milán

Authors
  1. Antonio Martínez
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  2. Francisco Milán
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Correspondence to Francisco Milán.

Additional information

Research partially supported by Ministerio de Educación Grant Nos: MTM2010-19821, PHB2010-0109, Junta de Andalucía Grant Nos. FQM-325 and P09-FQM-5088.

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Martínez, A., Milán, F. Flat fronts in hyperbolic 3-space with prescribed singularities. Ann Glob Anal Geom 46, 227–239 (2014). https://doi.org/10.1007/s10455-014-9420-6

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  • DOI: https://doi.org/10.1007/s10455-014-9420-6

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