Euler-Poincaré reduction on frame bundles

摘要

Let μ:FX→X be a principal bundle of frames with the structure group Gln(R) and let λ be a Gln(R)-invariant Lagrangian on J1FX. We give an explicit expressions of reduced equations for the associated sections of the corresponding bundle of linear connections which replace the Euler-Lagrange equations for the variational problem defined by λ.