We derive an interacting quintessence model on the framework of a recently introduced new class of geometrical scalar-tensor theories of gravity formulated on a Weyl-Integrable geometry, where the gravitational sector is described by both a scalar and a tensor metric field. By using a Palatini variational principle we construct a scalar-tensor action invariant under the Weyl symmetry group of the background geometry, which in the Einstein-Riemann frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the theory and the fact that the Weyl scalar field couples with matter fields to formulate an interacting quintessential model with a non-canonical kinetic term, where the quintessence field has a geometrical origin. Due to this non-canonicity we obtain that the mass of the quintessence field in the past epochs results to be small enough not to cause modifications in the baryon to photon ratio during nucleosynthesis.

6 pages, no-figures. Improved version. We have included a quintessence model