  By analyzing the vectorial Helmholtz equation within the thin-layer approach,
we find that light acquires a novel geometrical phase, in addition to the usual
one (the optical Berry phase), during the propagation along a curved path.
Unlike the optical Berry phase, the novel geometrical phase is induced by the
transverse spin along the binormal direction and associated with the curvature
of the curve. Furthermore, we show a novel Hall effect of light induced by the
torsion of the curve and associated with the transverse spin along the binormal
direction, which is different from the usual spin Hall effect of light.
Finally, we demonstrate that the usual and novel geometrical phase phenomena
are described by different geometry-induced U(1) gauge fields in different
adiabatic approximations. In the nonadiabatic case, these gauge fields are
united in one effective equation by SO(3) group.
