A geometric interpretation of the spectral parameter for surfaces of constant mean curvature
Abstract
Considering the kinematics of the moving frame associated with a constant mean curvature 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 -> infinity.
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