Generalized symmetric spaces, Yu. P. Solovyov's formula, and the generalized Hermitian geometry

We collect some basic results on canonical affinor structures of classical types on generalized symmetric spaces. Yu. P. Solovyov's stimulating influence on this topic during its first stage is illustrated. Using special canonical $f$-structures on homogeneous $k$-symmetric spaces, we also present a new collection of homogeneous Hermitian $f$-manifolds.