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

J L Cieśliński
2006 Journal of Nonlinear Mathematical Physics  
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.
doi:10.2991/jnmp.2006.13.4.5 fatcat:42selvgrazaipevvm6xchvqjei