2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169229The question of whether or not the set of Zoll metrics on the 2-sphere is connected is still open. Here we show that a naive application of the Ricci flow is not sufficient to answer this problem.5 pages, very lightDifferential Geometry53D25, 53C44The Ricci flow does not preserve the set of Zoll metricstext