Trilinear generally covariant equations

Abstract

Field equations for n-frames h ^a_μ that are possible in the theory of absolute parallelism are considered. It is shown that in three cases the equations can, after the substitution h ^a_μ =H^pH ^a_μ (H=det H ^a_μ , p is an n-dependent constant), be written in a trilinear form that contains only the matrix H ^μ_a and its derivatives and not H ^a_μ . It is shown that the equations are still regular for degenerate but finite matrices H ^μ_a if rank H ^μ_a ≥2.