Harmonic reductions in principal fibre bundles

On a principal fibre bundle P(M, G), with G a reductive Lie group, a variational principle is defined for the symmetry breaking Higgs fields to select certain subbundles of P(M, G). The splitting of the connection in terms of a tensorial 1-form on the subbundle is used to replace the Higgs fields and to define a new functional that leads naturally to the concept of harmonic reduction. The first variation is obtained and an application of this concept is given.