Orientational order, topology, and vesicle shapes

While ideal fluid membranes are characterized solely by curvature elasticity, many structural (``external'') properties of real membranes are strongly influenced by internal degrees of freedom. Here, we consider, within mean-field theory, the effect of in-plane vector order (such as the molecular tilt in surfactant bilayers) on the shapes of closed vesicles with the topology of a sphere. We find that coupling between in-plane order and Gaussian curvature causes continuous shape changes from spherical to cylindrical vesicles as the degree of in-plane order increases.