Mixed 3-Sasakian Statistical Manifolds and Statistical Submersions

Mixed 3-structures are known to be the counterpart in odd dimension of the quaternionic structures of second kind, also termed in the literature as paraquaternionic structures. The aim of this paper is to investigate the statistical structures in paraquaternionic and mixed 3-Sasakian geometry. We derive the main properties of statistical manifolds equipped with such kind of structures, focusing on the case of mixed 3-Sasakian statistical manifolds and paraquaternionic Kähler-like statistical manifolds. Moreover, we investigate the geometry of statistical submersions with total space a mixed 3-Sasakian manifold or a paraquaternionic Kähler-like statistical manifold. Moreover, we provide some illustrative examples.