Einstein–Hilbert Lagrangian Induced on the Linear Frame Bundle

Abstract

Let \(p_F :FN \rightarrow N\) be the bundle of linear frames of a \(C^\infty \) manifold N. The Lagrangian induced on FN by the Einstein–Hilbert Lagrangian is written as a differentiable function of the system of \(\mathrm {Diff}N\)-invariant Lagrangian defined on the linear frame bundle.