2021-04-122013-01-010302974316113349SCOPUS;2-s2.0-84884972071http://hdl.handle.net/10784/27665For 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 a-connections appears as special case of the q-connections ?(q). The main result is the expected one, namely the zero curvature of the manifold. © 2013 Springer-Verlag.enghttps://v2.sherpa.ac.uk/id/publication/issn/0302-9743info:eu-repo/semantics/conferencePaperFisher information metricFunctionalsLebesgue spaceNon-parametricRiemannian geometryBanach spacesFisher information matrixInformation scienceGeometry2021-04-12Loaiza, G.Quiceno, H.R.10.1007/978-3-642-40020-9_82