A geometric interpretation of the spectral parameter for surfaces of constant mean curvature

Details A geometric interpretation of the spectral parameter for surfaces of constant mean curvature A geometric interpretation of the spectral parameter for surfaces of constant mean curvature

2006-06-02

arxiv.org/abs/nlin/0606009v1

Journal of Nonlinear Mathematical Physics, 2006

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages

Scientific paper

Considering the kinematics of the moving frame associated with a constant mean curvature surface immersed in S^3 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 S^3. The application of the Sym formula to this linear problem yields constant mean curvature surfaces in E^3. Independently, we show that the Sym formula itself can be derived by an appropriate limiting process R -> infinity.

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