Superfícies Weingarten generalizada tipo harmônico no espaço hiperbólico - Fernandes, Karoline Victor (2013)
In this work we study surfaces M in hyperbolic space whose mean curvature H and Gaussian curvature KI satisfy the relation 2(H 1)e2μ +KI(1e2μ) = 0; where μ is a harmonic function with respect to the quadratic form s = KII + 2(H 1)II; and I, II denote, respectively, the first and second quadratic form of M. These surfaces are called Generalized Weingarten surfaces of harmonic type (HGW-surfaces). We obtain a representation type Weierstrass for these surfaces that depend on three holomorphic functions. As an application we obtain a representation type Weierstrass for Bryant surfaces and classify all HGW-surfaces of rotation.