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Minimal Darboux transformations

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Abstract

We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-sphere and flat fronts in hyperbolic space.

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Acknowledgments

The second author expresses his gratitude to the members of the Institute of Discrete Mathematics and Geometry at TU Wien for their hospitality during his stay in 2015/16.

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Authors and Affiliations

  1. Vienna University of Technology, Wiedner Hauptstraße 8–10/104, 1040, Vienna, Austria

    Udo Hertrich-Jeromin

  2. Miyakonojo College, National Institute of Technology, Yoshio, Miyakonojo, 885-8567, Japan

    Atsufumi Honda

Authors
  1. Udo Hertrich-Jeromin
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  2. Atsufumi Honda
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Corresponding author

Correspondence to Atsufumi Honda.

Additional information

This work has been partially supported by the Austrian Science Fund (FWF) and the Japan Society for the Promotion of Science (JSPS) through the FWF/JSPS Joint Project Grant I1671-N26 “Transformations and Singularities”.

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Hertrich-Jeromin, U., Honda, A. Minimal Darboux transformations. Beitr Algebra Geom 58, 81–91 (2017). https://doi.org/10.1007/s13366-016-0301-y

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  • DOI: https://doi.org/10.1007/s13366-016-0301-y

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