  The law of transformation of affine connection for n-dimensional manifolds as
the system of nonlinear equations on local coordinates of manifold is
considered. The extension of the Darboux-Lame system of equations to the spaces
of constant negative curvature is demonstrated. Geodesic deviation equation as
well as the equations of geodesics are presented in the form of the matrix
Darboux-Lame system of equations.
