Hyperbolicity of a class of first-order quasilinear covariant equations of divergent type

A special class of systems of first-order quasilinear partial differential equations is considered. These divergent-type systems are invariant under time and space translations; they are transformed covariantly under the action of the rotation group. We give a description of the class of nonlinear first-order differential operators corresponding to the systems of the considered class and prove a theorem on the equivalence of the concepts of hyperbolicity and hyperbolicity in the sense of Friedrichs.