论文标题
均质的非分类$ 3 $ - $（α，δ）$ - sasaki歧管和浸入QuaternionicKähler空间
Homogeneous non-degenerate $3$-$(α,δ)$-Sasaki manifolds and submersions over quaternionic Kähler spaces
论文作者
论文摘要
我们表明，每$ 3 $ - $（α，δ）$ - 尺寸的sasaki歧管$ 4N + 3 $承认本地定义的riemannian浸入量子的QuaternionicKähler折叠率16n（n + 2）αδ$。在非脱位情况（$δ\ neq 0 $）中，我们描述了所有同质$ 3 $ - $（α，δ）$ -Sasaki-sasaki-sasaki在对称的狼空间（case $αΔ> 0 $）上的纤维流动，并在他们的非竞争双对称空间（case $αΔ<0 $）上。如果$αδ> 0 $，则会产生均质$ 3 $ - $（α，δ）$ -Sasaki歧管的完整分类；对于$αδ<0 $，我们提供了均匀的$ 3 $ - $（α，δ）$ - sasaki歧管的一般结构，这是非对称Alekseevsky空间上的纤维，这是$ 19 $的最低维度。
We show that every $3$-$(α,δ)$-Sasaki manifold of dimension $4n + 3$ admits a locally defined Riemannian submersion over a quaternionic Kähler manifold of scalar curvature $16n(n+2)αδ$. In the non-degenerate case ($δ\neq 0$) we describe all homogeneous $3$-$(α,δ)$-Sasaki manifolds fibering over symmetric Wolf spaces (case $αδ> 0$) and over their the noncompact dual symmetric spaces (case $αδ< 0$). If $αδ> 0$, this yields a complete classification of homogeneous $3$-$(α,δ)$-Sasaki manifolds; for $αδ< 0$, we provide a general construction of homogeneous $3$-$(α,δ)$-Sasaki manifolds fibering over nonsymmetric Alekseevsky spaces, the lowest possible dimension of such a manifold being $19$.
