where "R""E" is the scalar curvature on the bundle as a whole (obtained from the metric *g+kω above), and "R"M("g") is the scalar curvature on the base manifold "M" (the Lagrangian density of the Einstein–Hilbert action), and "L"("g", ω) is the Lagrangian density for the Yang–Mills action, and "R""G"("k") is the scalar curvature on each fibre (obtained from the fiber metric "k", and constant, due to the Ad("G")-invariance of the metric "k"). The arguments denote that "R"M("g") only depends on the metric "g" on the base manifold, but not ω or "k", and likewise, that "R""G"("k") only depends on "k", and not on "g" or ω, and so-on.