Surfaces with mean of the hyperbolic curvature radii of double harmonic type

Abstract

In this paper, we define surfaces with mean of the hyperbolic curvature radii of double harmonictype (in short DHRMC-surfaces) in the hyperbolic space, these surfaces include the generalizedWeingarten surfaces of the harmonic type (HGW-surfaces). We give a characterization of DHRMC-surfaces. Given a real function, we will present a family of DHRMC-surfaces that depend on twoholomorphic functions. Moreover, we classify the DHRMC-surfaces of rotation.