Abstract.
A hyperbolic linear Weingarten surface in ℝ3 is a surface M whose mean and Gaussian curvatures satisfy the relationship 2aH +bK = c for real numbers a, b, c such that a2+bc < 0. In this work we obtain a representation for such a surface in terms of its Gauss map when, more generally, a, b, c are functions on M. We also study the completeness of such surfaces and describe a procedure to construct complete examples from solutions of the sine-Gordon equation.
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The first author is partially supported by Junta de Comunidades de Castilla-La Mancha, Grant no. PAI-05-034. The first and second authors are partially supported by Ministerio de Education y Ciencia Grant No. MTM2004-02746.
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Aledo Sánchez, J.A., Espinar, J.M. Hyperbolic linear Weingarten surfaces in ℝ3. Bull Braz Math Soc, New Series 38, 291–300 (2007). https://doi.org/10.1007/s00574-007-0047-0
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DOI: https://doi.org/10.1007/s00574-007-0047-0