On integrability conditions of derivation equations in a subspace of asymmetric affine connection space

In a space $L_N$ of asymmetric affine connection by equations (1.1) a submanifold $X_M\subset L_N$ is defined. On $X_M$ and on pseudonormal submanifold $X_{N-M}^N$ asymmetric induced connections are defined. Because of asymmetry of induced connection it is possible to define four kinds of covariant derivative. In this work we are considering integrability conditions of derivational equations \cite{4} obtained by help of the $1^{st}$ and the $2^{nd}$ kind of covariant derivative. The corresponding Gauss-Codazzi equations are obtained too.