Bobenko, A. and Eitner, U. (1998) Bonnet Surfaces and Painlevé Equations. Journal für die reine und angewandte Mathematik, 499, 47-79.
https://doi.org/10.1515/crll.1998.061

has been cited by the following article:

• TITLE: Helicoidal Surfaces and Their Relationship to Bonnet Surfaces

  AUTHORS: Paul Bracken

  KEYWORDS: Surface, Fundamental Forms, Structure Equations, Mean Curvature, Bonnet, Helicoidal

  JOURNAL NAME: Advances in Pure Mathematics, Vol.7 No.1, January 24, 2017

  ABSTRACT: An important question that arises is which surfaces in three-space admit a mean curvature preserving isometry which is not an isometry of the whole space. This leads to a class of surface known as a Bonnet surface in which the number of noncongruent immersions is two or infinity. The intention here is to present a proof of a theorem using an approach which is based on differential forms and moving frames and states that helicoidal surfaces necessarily fall into the class of Bonnet surfaces. Some other results are developed in the same manner.