On Sections of Complex Line Bundles over Surfaces Minimizing a Ginzburg–Landau Energy

In this work, we extend some of the results of Ignat and Jerrard (Arch Ration Mech Anal 239(3):1577–1666, 2021) for Ginzburg–Landau vortices of tangent vector fields on 2-dimensional Riemannian manifolds to the setting of complex Hermitian line bundles. In particular, we elucidate the locations of vortices for the cases of Q-tensors and their higher-rank analogs on a sphere. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.