Graph-type biharmonic surfaces in R3

Abstract

In this work, we study biharmonic surfaces that are parameterized by biharmonic coordinate functions. We study a class of biharmonic surfaces called graph-type biharmonic surfaces. Also, we define a class of surfaces associated to two harmonic functions (FH2A-surfaces), these surfaces satisfy a relation between the Gaussian curvature, the projection of the Gauss map on a fixed plane and two harmonic functions. We show that a particular class of graph-type biharmonic surfaces are FH2A-surfaces. Finally, we classify the FH2A-surfaces of rotation.

Keywords

• biharmonic surfaces
• harmonic surfaces
• gaussian curvature