  We report a new type of spin-orbit coupling (SOC) called geometric SOC.
Starting from the relativistic theory in curved space, we derive an effective
nonrelativistic Hamiltonian in a generic curve embedded into flat three
dimensions. The geometric SOC is $O(m^{-1})$, in which $m$ is the electron
mass, and hence much larger than the conventional SOC of $O(m^{-2})$. The
energy scale is estimated to be a hundred meV for a nanoscale helix. We
calculate the current-induced spin polarization in a coupled-helix model as a
representative of the chirality-induced spin selectivity. We find that it
depends on the chirality of the helix and is of the order of $0.01 \hbar$ per
${\rm nm}$ when a charge current of $1~{\rm \mu A}$ is applied.
