Algebraic dependences of Gauss maps of algebraic complete minimal surfaces sharing hyperplanes without counting multiplicities

Abstract

The aim of this paper is to give some algebraic dependences theorems for the Gauss maps of algebraic complete minimal surfaces sharing hyperplanes in projective without counting multiplicity, where all zeros with multiplicities more than a certain number are omitted. As a consequence, we obtain some results on uniqueness problem of Gauss maps of algebraic complete minimal surfaces which generalize and improve a known result of  L. Jin - M. Ru \cite{JR}.