  The Geometrical Localization mechanism in Randall-sundrum (RS) scenarios is
extended by considering the coupling between a quadratic mass term and
geometrical tensors. Since the quadratic term is symmetric, tensors with two
symmetric indices have to be taken into account. These are the Ricci and the
Einstein tensors. For the Ricci tensor it is shown that a localized zero mode
exists while that is not possible for the Einstein tensor. It is already known
that the Ricci scalar generates a localized solution but the metrics do not.
Therefore, it can be conclude that divergenceless tensors do not localize the
zero mode of gauge fields. The result is valid for any warp factor recovering
the RS metrics at the boundaries, and therefore is valid for RS I and II
models. We also compute resonances for all couplings. These are calculated
using the transfer matrix method. The cases studied consider the standard RS
with delta-like branes, and branes generated by kinks and domain-wall as well.
The parameters are changed to control the thickness of the smooth brane. We
find that, for all cases considered, geometrical coupling does not generate
resonances. This enforces similar results for the coupling with the Ricci
scalar and points to the existence of some unidentified fundamental structure
of these couplings.
