Generalized quasi-statistical structures

Given a non-degenerate (0, 2)-tensor field h on a smooth manifold M , we consider a natural generalized complex and a generalized product structure on the generalized tangent bundle T M ⊕ T ∗ M of M and we show that they are ∇-integrable, for ∇ an affine connection on M, if and only if (M,h,∇) is a quasi-statistical manifold. We introduce the notion of generalized quasi-statistical structure and we prove that any quasi-statistical structure on M induces generalized quasi-statistical structures on T M ⊕ T ∗ M . In this context, dual connections are considered and some of their properties are established. The results are described in terms of Patterson-Walker and Sasaki metrics on T∗M, horizontal lift and Sasaki metrics on TM and, when the connection ∇ is flat, we define the prolongations of the quasi-statistical structures on the manifolds to their cotangent and tangent bundles via Generalized Geometry. Moreover, Norden and Para-Norden structures are defined on T∗M and TM.