  In the braneworld scenario, the four dimensional effective Einstein equation
has extra terms which arise from the embedding of the 3-brane in the bulk.
These non-local effects, generated by the free gravitational field of the bulk,
may provide an explanation for the dynamics of the neutral hydrogen clouds at
large distances from the galactic center, which is usually explained by
postulating the existence of the dark matter. We obtain the exact galactic
metric, the dark radiation and the dark pressure in the flat rotation curves
region in the brane world scenario. Due to the presence of the bulk effects,
the flat rotation curves could extend several hundred kpc. The limiting radius
for which bulk effects are important is estimated and compared with the
numerical values of the truncation parameter of the dark matter halos, obtained
from weak lensing observations. There is a relatively good agreement between
the predictions of the model and observations. The deflection of photons is
also considered and the bending angle of light is computed. The bending angle
predicted by the brane world models is much larger than that predicted by
standard general relativistic and dark matter models. The angular radii of the
Einstein rings are obtained in the small angles approximation. The predictions
of the brane world model for the tangential shear are compared with the
observational data obtained in the weak lensing of galaxies in the Red-Sequence
Cluster Survey. Therefore the study of the light deflection by galaxies and the
gravitational lensing could discriminate between the different dynamical laws
proposed to model the motion of particles at the galactic level and the
standard dark matter models.
