The Hyperbolic Geometry of the Sinh - Gordon Equation Preprint
نویسنده
چکیده
This preliminary report studies immersed surfaces of constant mean curvature in H through their adjusted Gauss maps (as harmonic maps in S) 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. Mathematics Subject Classification: 53A10, 58E20
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