  Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are
known to give rise to several special geometries, whose complexity and beauty
continue to fascinate us, as observers of the natural world, and challenge us
as scientists. Here I show that a special class of surfaces of constant
negative Gaussian curvature can be obtained in fluid interfaces equipped with
an orientational ordered phase. These arise in various soft and biological
materials, such as nematic liquid crystals, cytoskeletal assemblies, or hexatic
colloidal suspensions. The purely hyperbolic morphology originates from the
competition between surface tension, that reduces the area of the interface at
the expense of increasing its Gaussian curvature, and the orientational
elasticity of the ordered phase, that in turn suffers for the distortion
induced by the underlying curvature.
