“…25 Curvature driven dynamics also play an important role in different biological processes [26][27][28] as well as in different properties of colloidal systems. [29][30][31] Three dimensional uniaxial nematics are orientationally ordered fluids, and can be characterized by the three component unit director n ˆ= (n x (x,y,z),n y (x,y,z),n z (x,y,z)), whereas the unit director of two dimensional a Centre for Condensed Matter Theory, Department of Physics, Indian Institute of nematics in a plane has two components: n ˆ= (n x (x,y),n y (x,y)). On a curved surface such as a sphere, the two dimensional nematic director lies in the local tangent plane to the sphere.…”