Polly, D. F. (2017). Linear Weingarten channel surfaces [Diploma Thesis, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/80102
E104 - Institut für Diskrete Mathematik und Geometrie
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Date (published):
2017
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Number of Pages:
41
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Keywords:
channel surface; linear Weingarten surface; sphere geometry
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Abstract:
Every linear Weingarten channel surface in Euclidean 3-space is either tubular or parallel to a surface of revolution. In this thesis we take a first step towards a generalization of this result to surfaces in the 3-sphere or in hyperbolic 3-space: We prove that non-tubular linear Weingarten channel surfaces in any space form can be projected to Euclidean space such that the resulting surface is part of a cylinder, a cone or a surface of revolution. To do this, we explore how linear Weingarten surfaces appear as special Omega-surfaces in Lie sphere geometry.