On Degenerate 3-(<i>α</i>, <i>δ</i>)-Sasakian Manifolds

We propose a new method to construct degenerate $3$-$(\alpha,\delta)$-Sasakian manifolds as fiber products of Boothby-Wang bundles over hyperk\"ahler manifolds. Subsequently, we study homogeneous $3$-$(\alpha, \delta)$-Sasakian and prove that no non-trivial compact examples exist well there is exactly one family nilpotent Lie groups with this geometry, the quaternionic Heisenberg groups.