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In two dimensional nematics, topological defects are point like singularitieswith both a charge and a phase. We study topological defects within curvednematic textures on the surface of a cylinder. This allows us to isolate theeffect of extrinsic curvature on the structure of the topological defect. Byminimizing the energy associated with distortions in the nematic directoraround the core of a defect we show that the phase of the topological defect iscoupled to the orientation of the cylinder. This coupling depends on therelative energetic cost associated with splay, bend and twist distortions ofthe nematic director. We identify a bistability in the phase of the defectswhen twist deformations dominate. Finally, we show a similar effect for integercharge topological defects.

Coupling topological defect phase to extrinsic curvature in nematic shells