Author:
Agricola Ilka,Dileo Giulia,Stecker Leander
Abstract
AbstractWe show that every 3-$$(\alpha ,\delta )$$
(
α
,
δ
)
-Sasaki manifold of dimension $$4n + 3$$
4
n
+
3
admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature $$16n(n+2)\alpha \delta$$
16
n
(
n
+
2
)
α
δ
. In the non-degenerate case we describe all homogeneous 3-$$(\alpha ,\delta )$$
(
α
,
δ
)
-Sasaki manifolds fibering over symmetric Wolf spaces and over their non-compact dual symmetric spaces. If $$\alpha \delta > 0$$
α
δ
>
0
, this yields a complete classification of homogeneous 3-$$(\alpha ,\delta )$$
(
α
,
δ
)
-Sasaki manifolds. For $$\alpha \delta < 0$$
α
δ
<
0
, we provide a general construction of homogeneous 3-$$(\alpha , \delta )$$
(
α
,
δ
)
-Sasaki manifolds fibering over non-symmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being 19.
Funder
Philipps-Universität Marburg
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
Reference20 articles.
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