Villarceau foliated solitons in the two-dimensional O(3) nonlinear sigma model

We obtain the complete space of solutions, in the two-dimensional O(3) nonlinear sigma model, which are foliated by Villarceau circles. In particular, we prove the existence of solitons that admit a foliation by nonparallel circles. This contrasts with the Plateau context, where solitons foliated by nonparallel circles cannot exist. These solitons carry topological charges that are holographically computed via the Gauss-Bonnet formula.