Nearly Kähler and Hermitian \(f\)-structures on homogeneous \(k\)-symmetric spaces (Q610567)

The aim of this paper is to show that all the base canonical \(f\)-structures on naturally reductive \(k\)-symmetric spaces (where \(k\geq 3\)) are nearly Kähler \(f\)-structures. The authors give a criterion for a canonical \(f\)-structure to be the sum or difference of two base \(f\)-structures to be nearly Kähler. They describe those base \(f\)-structures which are also Hermitian and they give a criterion for the remaining base structures to be Hermitian. The paper is very short. It contains the basic definitions and main results. The proofs are not completely worked out but only sketched.