  The interplay between order and geometry in soft condensed matter systems is
an active field with many striking results and even more open problems. Ordered
structures on curved surfaces appear in multi-electron helium bubbles, viral
and bacteriophage protein capsids, colloidal self-assembly at interfaces and in
physical membranes. Spatial curvature can lead to novel ground state
configurations featuring arrays of topological defects that would be excited
states in planar systems. We illustrate this with a sequence of images showing
the Voronoi lattice (in gold) and the corresponding Delaunay triangulations (in
green) for ten low energy configurations of a system of classical charges
constrained to lie on the surface of a paraboloid and interacting with a
Coulomb potential. The parabolic geometry is considered as a specific
realization of the class of crystalline structures on two-dimensional
Riemannian manifolds with variable Gaussian curvature and boundary.
