  The gravitational equations of the three dimensional (3D) brane world are
investigated for both off-diagonal and warped 5D metrics which can be
diagonalized with respect to some anholonomic frames when the gravitational and
matter fields dynamics are described by mixed sets of holonomic and anholonomic
variables. We construct two new classes of exact solutions of Kaluza-Klein
gravity which generalize the Randall-Sundrum metrics to configurations with
running on the 5th coordinate gravitational constant and anisotropic
dependencies of effective 4D constants on time and/or space variables. We
conclude that by introducing gauge fields as off-diagonal components of 5D
metrics, or by considering anholonomic frames modelling some anisotropies in
extra dimension spacetime, we induce anisotropic tensions (gravitational
polarizations) and running of constants on the branes. This way we can generate
the TeV scale as a hierarchically suppressed anisotropic mass scale and the
Newtonian and general relativistic gravity are reproduced with adequate
precisions but with corrections which depend anisotropically on some
coordinates.
