  Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed
with an in-plane nematic order. In 2012, two variational models have been
introduced by Giomi [10] and by Napoli and Vergori [27,26]. Both penalize the
area of the surface and the gradient of the director: in [10] the covariant
derivative of the director is considered, while [26] deals with the surface
gradient. In this paper, a complete variational analysis of the model proposed
by Giomi is performed for revolution surfaces spanning two coaxial rings.
