Homogeneous non-degenerate $3$-$(\alpha ,\delta )$-Sasaki manifolds and submersions over quaternionic Kähler spaces

Abstract

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 ($\delta \ne 0$) we describe all homogeneous $3$-$(\alpha ,\delta )$-Sasaki manifolds fibering over symmetric Wolf spaces (case $\alpha \delta >0$) and over their the noncompact dual symmetric spaces (case $\alpha \delta <0$). 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 nonsymmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being $19$.

25 pages, 2 tables

Cited by in corpus (4)

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