Zeilinger, J. (2020). Surfaces of constant mean curvature 1 in hyperbolic 3-space : the Bianchi-Calò method and Darboux transforms [Diploma Thesis, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/79938
E104 - Institut für Diskrete Mathematik und Geometrie
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Datum (veröffentlicht):
2020
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Umfang:
23
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Keywords:
constant mean curvature; hyperbolic space; Weierstrass type representation; Darboux transformation
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Abstract:
We construct cmc-1 surfaces in the Poincare half-space model of hyperbolic 3-space in terms of their hyperbolic Gauss maps via 1) the Bianchi-Calo method - leading to an explicit parametrization - and via 2) Darboux transforms. We then connect the two approaches.
