Naturally reductive almost product manifolds

Vitaly V. Balashchenko


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