  Generalized $(\kappa ,\mu )$ structures occur in dimension 3 only. In this
dimension 3, only K-contact structures can occur as generalized Eta-Einstein.
On closed manifolds, Eta-Einstein, K-contact structures which are not
D-homothetic to Einstein structures are almost regular. We also construct
examples of compact, generalized Jacobi $(\kappa ,\mu )$-structures.
