Affine Submanifolds of Rank Two

In the paper we study the complete connected affine submanifolds $f:M^n \rightarrow {\mathbb{R}}^{n+m}$ of rank two, i.e., the strongly ($n-2)$-parabolic submanifolds according to A. Borisenko. The structures of these submanifolds are described and the explicit parametrization is given for two partial cases.