Geometrical approach to the gauge field mass problem. Possible reasons for which the Higgs bosons are unobservable

The (4+d)-dimensional Einstein--Hilbert gravity action is considered in the Kaluza - Klein approach. The extra-dimensional manifold Vd is a Riemannian space with the d-parametric group of isometries Gd which acts on Vd by the left shifts and with an arbitrary non-degenerate left-invariant metric gab. The gauge fields A-barμ(x) are introduced as the affine connection coefficients of the fiber bundle with Vd being the fiber. The effective Lagrangian Leff{A-barμ(x), gab} is obtained as an invariant integral of the curvature scalar of the structure considered. The conditions on gab are formulated under which Leff{Aμ-bar(x), gab} contains in addition to the square of the gauge field strength tensor also the quadratic form of Aμ-bar(x) and additional fields with pure gauge degrees of freedom. The eigenvalues of the quadratic form are calculated for the case of the gauge group SO(3) and it is shown that they are not equal to zero in the case when gab is not proportional to the unit matrix