Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. In this paper we have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.