Novas classes de superfícies Weingarten generalizadas

Abstract

In this work, we define surfaces with double harmonic mean curvature of the radial type - CMRHD surfaces - in hyperbolic space. These surfaces encompass generalized Weingarten surfaces of harmonic type - WGH surfaces - and are defined based on one real function and two harmonic functions. We obtain families of these surfaces that depend on two holomorphic functions. As an application, we provide a parametrization for the rotational case. We also define generalized Weingarten surfaces of harmonic type II - WGHII surfaces - and present families of these surfaces that depend on two holomorphic functions. As an application, we provide a parametrization for the rotational case and analyze the behavior of the generatrix curve.