Volume 13, Issue 4, November 2006, Pages 507 - 515
A geometric interpretation of the spectral parameter for surfaces of constant mean curvature
Authors
J.L. Cieśliński
Corresponding Author
J.L. Cieśliński
Received 15 December 2005, Accepted 2 June 2006, Available Online 1 November 2006.
- DOI
- 10.2991/jnmp.2006.13.4.5How to use a DOI?
- Abstract
Considering the kinematics of the moving frame associated with a constant mean cuvature surface immersed in S3 we derive a linear problem with the spectral parameter corresponding to elliptic sinh-Gordon equation. The spectral parameter is related to the radius R of the sphere S3 . The application of the Sym formula to this linear problem yields constant mean curvature surfaces in E3 . Independently, we show that the Sym formula itself can be derived by an appropriate limiting process R .
- Copyright
- © 2006, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - J.L. Cieśliński PY - 2006 DA - 2006/11/01 TI - A geometric interpretation of the spectral parameter for surfaces of constant mean curvature JO - Journal of Nonlinear Mathematical Physics SP - 507 EP - 515 VL - 13 IS - 4 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2006.13.4.5 DO - 10.2991/jnmp.2006.13.4.5 ID - Cieśliński2006 ER -