Abstract
Similar to Chapter 3, one considers the Bonnet problem in S 3 and H 3. The local theory of Bonnet surfaces in S 3 and H 3 without critical points of the mean curvature function was developed in [Vo], [ChL]. It was proven that all Bonnet surfaces in S 3 are Weingarten surfaces, and a classification similar to Cartan’s classification of Bonnet surfaces in ℝ3 was obtained. The Gauss-Codazzi equations of Bonnet surfaces in S 3 reduce to an ordinary differential equation similar to (3-18):
), with C > 0.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2000). 4. Bonnet Surfaces in S 3 and H 3 and Surfaces with Harmonic Inverse Mean Curvature. In: Bobenko, A.I., Eitner, U. (eds) Painlevé Equations in the Differential Geometry of Surfaces. Lecture Notes in Mathematics, vol 1753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44452-1_4
Download citation
DOI: https://doi.org/10.1007/3-540-44452-1_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41414-8
Online ISBN: 978-3-540-44452-7
eBook Packages: Springer Book Archive