Laguerre Type Surfaces

Abstract

In this work we introduce the Laguerre type surfaces, this class of surfaces contains the minimal surfaces, another class of these surfaces are the Weingarten surfaces of Laguerre type. We show that all graph- type harmonic surfaces are Laguerre type surfaces. As an application we classify the graph-type harmonic surfaces that are Weingarten surfaces of Laguerre type and also we classify the graph-type harmonic surfaces that are helicoidal. We present families of cyclic graph-type harmonic surfaces type with the planes of the foliation parallel. Finally, we give a classification of translation surfaces of Laguerre type.