Nearly Kähler and Hermitian f-structures on homogeneous k-symmetric spaces

Abstract

In this paper, we show that all of the base canonical f-structures on naturally reductive k-symmetric spaces (where k ≥ 3) are nearly Kähler f-structures. We also give a criterion for a canonical f-structure being the sum or difference of two base f-structures to be nearly Kähler. We describe those base f-structures which are also Hermitian f-structures and give a criterion for the remaining base structures to be Hermitian. The results obtained in this paper are of general character and imply some of the previous results as corollaries. By way of example, results on canonical f-structures on homogeneous 6-symmetric spaces are deduced.