  The mechanics of a flexible membrane decorated with a nematic liquid-crystal
texture is considered in a variational framework. The variations on the splay,
twist and the bend energy of the nematics are obtained from the local
deformations leading to changes in the shape membrane. The Euler-Lagrange
derivatives and the Noether charges are identified from the variational
equations. The nematic stress tensor is obtained as a consequence of
translational invariance. Likewise, the rotational invariance implies the
torque nematic tensor. The corresponding boundary conditions are obtained for
free edges in the open-membrane configuration. These results constitute the
basis of a generalized theory of elasticity for anisotropic nematic membranes.
Some relevant consequences of the presence of nematic ordering are visualized
at revolution surfaces with axial symmetry.
