Invariant f-structures in generalized Hermitian geometry

Abstract

We collect the recent results on invariant f-structures in generalized Hermitian geometry. Here the canonical f-structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f-structures, Hermitian f-structures and some others. Finally, we consider all invariant f-structures on the complex flag manifold SU(3)/Tmax and describe them in the sense of generalized Hermitian geometry. In particular, we present first invariant examples of Killing f-structures.