  Recent theoretical and experimental works on carbon nanotubes and graphene
samples have revealed that spin-orbit interactions, though customarily ignored
in carbon-based materials, are more important and complex than it was thought.
We study the intrinsic spin-orbit coupling effects on graphene nanoribbons,
both flat and bent. Calculations are performed within the tight-binding model
with the inclusion of a four-orbital basis set. Thereby the full symmetry of
the honeycomb lattice and the hybridization of $\sigma$ and $\pi$ bands are
considered. In addition to the zero-energy $\pi$-edge states, $\sigma$-derived
edge states are found for the three investigated ribbon geometries. The
$\sigma$ states are also spin-filtered and localized at the boundaries of the
ribbons. The calculated spin-orbit splittings are larger for the $\sigma$- than
for the $\pi$-derived edge states. Due to this enhancement, spin-orbit
splittings of the $\sigma$-states reach values of the order of a few Kelvin.
These spin-filtered edge states are robust under $\sigma-\pi$ hybridization and
curvature effects.
