Geometries of Maximal Acceleration

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We 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 added

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