Surfaces with closed Möbius form

This paper is devoted to investigating the Möbius differential geometry of a new class of surfaces, named the surfaces with closed Möbius form. The main theorem shows that a surface with closed Möbius form can be determined by a smooth function satisfying a 5th order partial differential equation presented in this paper. As an application of the main theorem, the isothermic surfaces with closed Möbius form are classified.