Generally-covariant and \(GL(N,\mathbb{R})\)-invariant models of self-interacting field of linear frames (Q1372428)

Let \(e\) be a frame field on a manifold \(M\), i.e., a section of the linear frame bundle of \(M\). The author first constructs two tensor fields \(G\) and \(\gamma\) of type \((0,2)\) on \(M\) by means of the structure function of \(e\). These tensor fields are used for constructing generally covariant Lagrangians determined by \(e\). The corresponding field equations are deduced and some their solutions are described. The case that \(G\) and \(\gamma\) are nonsingular is studied in detail.