The Hyperbolic Geometry of the Sinh-Gordon Equation

Original · EN

This preliminary report studies immersed surfaces of constant mean curvature in H³ through their adjusted Gauss maps (as harmonic maps in S²) and their adjusted frames in SU(2). Lawson's correspondence between Euclidean CMC surfaces and their hyperbolic cousins is interpreted here under a different perspective: the equivalence of their Weierstrass representations (normalized potentials). This work also presents a construction algorithm for the moving frame, the adjusted frame, their Maurer-Cartan forms, and ultimately the CMC immersion.