Lax type representation for embeddings of manifolds in non-Riemannian enveloping spaces

The Gauss, Peterson–Codazzi, and Ricci equations are reformulated for embeddings of manifolds in non-Riemannian eveloping spaces in the form of a Lax representation in a two-dimensional space, this being achieved by realization of the corresponding operators in the algebra $gl(N,\mathbf R)$.