Invariant structures on the 6-dimensional generalized Heisenberg group

Vitaly V. Balashchenko

In this paper, using the theory of canonical structures on homogeneous $k$-symmetric spaces, we construct four left-invariant metric $f$-structures on the $6$-dimensional generalized Heisenberg group. It provides new invariant examples for the classes of nearly Kähler and Hermitian $f$-structures as well as almost Hermitian $G_1$-structures.