Abstract
Let c be a positive constant and H a constant satisfying |H| > c. Our primary object of this paper is to give representation formulas for branched CMC H (constant mean curvature H) surfaces in the hyperbolic 3-space ” 3(-c2) of constant curvature c2, and for spacelike CMC H surfaces in the de Sitter 3-space S 3 1(c2) of constant curvature c2. These formulas imply, for example, that every CMC H surface in ” 3(-c2) can be represented locally by a harmonic map to the unit 2-sphere S2.
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Aiyama, R., Akutagawa, K. Kenmotsu–Bryant Type Representation Formulas for Constant Mean Curvature Surfaces in ” 3(-c2) and S 3 1(c2). Annals of Global Analysis and Geometry 17, 49–75 (1999). https://doi.org/10.1023/A:1006504614150
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DOI: https://doi.org/10.1023/A:1006504614150