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arXiv · 1904.10930

A duality for Guichard nets

Gudrun Szewieczek
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Abstract

In this paper we study G-surfaces, a rather unknown surface class originally defined by Calapso, and show that the coordinate surfaces of a Guichard net are G-surfaces. Based on this observation, we present distinguished Combescure transformations that provide a duality for Guichard nets. Another class of special Combescure transformations is then used to construct a B\"acklund-type transformation for Guichard nets. In this realm a permutability theorem for the dual systems is proven.

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Gudrun Szewieczek. 2019-04-24. A duality for Guichard nets. https://arxiv.org/abs/1904.10930

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