  A continuum model for the effective spin orbit interaction in graphene is
derived from a tight-binding model which includes the $\pi$ and $\sigma$ bands.
We analyze the combined effects of the intra-atomic spin-orbit coupling,
curvature, and applied electric field, using perturbation theory. We recover
the effective spin-orbit Hamiltonian derived recently from group theoretical
arguments by Kane and Mele. We find, for flat graphene, that the intrinsic
spin-orbit coupling $\Hi \propto \Delta^ 2$ and the Rashba coupling due to a
perpendicular electric field ${\cal E}$, $\Delta_{\cal E} \propto \Delta$,
where $\Delta$ is the intra-atomic spin-orbit coupling constant for carbon.
Moreover we show that local curvature of the graphene sheet induces an extra
spin-orbit coupling term $\Delta_{\rm curv} \propto \Delta$. For the values of
$\cal E$ and curvature profile reported in actual samples of graphene, we find
that $\Hi < \Delta_{\cal E} \lesssim \Delta_{\rm curv}$. The effect of
spin-orbit coupling on derived materials of graphene, like fullerenes,
nanotubes, and nanotube caps, is also studied. For fullerenes, only $\Hi$ is
important. Both for nanotubes and nanotube caps $\Delta_{\rm curv}$ is in the
order of a few Kelvins. We reproduce the known appearance of a gap and
spin-splitting in the energy spectrum of nanotubes due to the spin-orbit
coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the
localized states at the cap, which could allow spin-dependent field-effect
emission.
