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Ítem A Riemannian Geometry in the q-Exponential Banach Manifold induced by q-Divergences.(Springer, 2013) Quiceno, H. R.; Loaiza, Gabriel; Universidad EAFIT. Escuela de Ciencias y Humanidades. Grupo de Investigación Análisis Funcional y Aplicaciones; Gabriel Loaiza (gloaiza@eafit.edu.co)For the family of non-parametric q-exponential statistical models, in a former paper, written by the same authors, a differentiable Banach manifold modelled on Lebesgue spaces of real random variables has been built. In this paper, the geometry induced on this manifold is characterized by q-divergence functionals. This geometry turns out to be a generalization of the geometry given by Fisher information metric and Levi-Civita connections. Moreover, the classical Amari’s α-connections appears as special case of the q −connections ∇ (q). The main result is the expected one, namely the zero curvature of the manifold.