  Within the framework of the well-known curvature models, a fluid lipid
bilayer membrane is regarded as a surface embedded in the three-dimensional
Euclidean space whose equilibrium shapes are described in terms of its mean and
Gaussian curvatures by the so-called membrane shape equation. In the present
paper, all solutions to this equation determining cylindrical membrane shapes
are found and presented, together with the expressions for the corresponding
position vectors, in explicit analytic form. The necessary and sufficient
conditions for such a surface to be closed are derived and several sufficient
conditions for its directrix to be simple or self-intersecting are given.
