Hyperbolic Linear Weingarten Surfaces in R3
2007 - J.A. Aledo, J.M. Espinar
Bulletin of the Brazilian Mathematical Society 38, 291-300 (2007).
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.