  An elastic membrane with embedded nematic molecules is considered as a model
of anisotropic fluid membrane with internal ordering. By considering the
geometric coupling between director field and membrane curvature, the nematic
texture is shown to induce anisotropic stresses additional to Canham-Helfrich
elasticity. Building upon differential geometry, analytical expressions are
found for the membrane stress and torque induced by splaying, twisting and
bending of the nematic director as described by the Frank energy of liquid
crystals. The forces induced by prototypical nematic textures are visualized on
the sphere and on cylindrical surfaces.
