Abstract. It is proved that, in accordance with the Naveira classification, there are exactly three classes of invariant naturally reductive almost product structures. A remarkable collection of such structures is presented. These structures are canonical almost product structures on Riemannian $k$-symmetric spaces. Some particular cases including non-naturally reductive the 6-dimensional generalized Heisenberg group are considered in more detail.
AMSclassification. Primary 53C15, 53C30; Secondary 53C10, 53C35
Keywords. Almost product structure, homogeneous space, naturally reductive space, $k$-symmetric space