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Homogeneous non-degenerate 3-(α,δ)-Sasaki manifolds and submersions over quaternionic Kähler spaces
Annals of Global Analysis and Geometry  (IF0.846),  Pub Date : 2021-04-26, DOI: 10.1007/s10455-021-09762-9
Ilka Agricola, Giulia Dileo, Leander Stecker

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