A duality for Guichard nets
Differential Geometry
2019-04-25 v1
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.
Cite
@article{arxiv.1904.10930,
title = {A duality for Guichard nets},
author = {Gudrun Szewieczek},
journal= {arXiv preprint arXiv:1904.10930},
year = {2019}
}
Comments
25 pages, 4 figures