  We derive the hydrodynamic equations for nematic liquid crystals lying on
curved substrates. We invoke the Lagrange-Rayleigh variational principle to
adapt the Ericksen-Leslie theory to two-dimensional nematics in which a
degenerate anchoring of the molecules on the substrate is enforced. The only
constitutive assumptions in this scheme concern the free-energy density, given
by the two-dimensional Frank potential, and the density of dissipation which is
required to satisfy appropriate invariance requirements. The resulting
equations of motion couple the velocity field, the director alignment and the
curvature of the shell. To illustrate our findings, we consider the effect of a
simple shear flow on the alignment of a nematic lying on a cylindrical shell.
