2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52285We discuss and compare several geometric structures which imply an upper bound to the acceleration of a particle measured in its rest system. While all of them have the same implications on the motion of a point particle, they differ in other important respects. In particular, they have different symmetry groups, which influence in a different way the search for an underlying dynamical theory.21 pages, LaTex, no figures, notations changed, some remarks and some new references addedHigh Energy Physics - Theorytext