Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
13 - 4
Pages
507 - 515
Publication Date
2006/11/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2006.13.4.5How to use a DOI?
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  -