Construction of the normal form of the equation of a surface of high codimension (Q2639200)

This paper is dedicated to a construction of the normal form of the equation of a surface of co-dimension \(k\geq 1\). The theorems on normalizing by formal series as well as partial normalizing are proved, which are like Theorems 2.2 and 3.1 of the \textit{S. S. Chern} and \textit{J. K. Moser}'s work in Acta Math. 133 (1974), 219-271 (1975; Zbl 0302.32015).