Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces

Abstract We show that every 3- $$(\alpha ,\delta )$$ ( α , δ ) -Sasaki manifold of dimension $$4n + 3$$ 4 n + 3 admits a locally defined Riemannian submersion over quaternionic Kähler scalar curvature $$16n(n+2)\alpha \delta$$ 16 2 . In the non-degenerate case we describe all homogeneous manifolds fibering symmetric Wolf spaces and their non-compact dual spaces. If $$\alpha \delta > 0$$ > 0 , this yields complete classification manifolds. For < < provide general construction non-symmetric Alekseevsky spaces, lowest possible such being 19.