









Nematics in nonspherical curved spaces
Samuele Elisei, Basil Soofi and Alberto FernandezNieves
Defects on spherical drops and shells have been already investigated and we are now interested in studying topology
of nematic phase on nonspherical spaces. The main reason for studying different geometries is that the number and type
of defects in a drop of Liquid Crystal is subject to the geometrical constraint that the total topological charge on the surface, i.e. the
sum of the charge of the single defects, must equal the Euler characteristic χ of the surface itself. The Euler characteristic can be expressed
in terms of the genus g of the surface that equals the number of “handles”
of the closed surface. χ = 2(1  g). That means that for a
sphere we will have χ = 2, on a torus χ = 0, on a figure eight χ = 2. Though on a torus the geometrical constraint allows the Liquid
Crystal to arrange in a way that doesn’t present any defect, it is possible that it will be energetically favorable for the nematic phase
to have defects: in that case we expect these defects’ charge to cancel out. The negative characteristic of the figure eight ensures that we
will need to have at least two defect of negative 2 charge.

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 303320430, USA
Phone: 4043853667 Fax: 4048949958
alberto.fernandez [at] physics.gatech.edu