Generally-covariant and GL(n, R)-invariant model of field of linear frames interacting with a multiplet of complex scalar fields

Generally-covariant and GL(n, R)-invariant theory of the field of linear frames interacting with a multiplet of complex scalar fields is presented. The invariance assumptions introduced into the theory result in a modified Born-Infeld-type nonlinearity of the model. A Lagrangian of the system is constructed, field equations are derived and three families of geometrically privileged solutions are found.