Quaternionic contact hypersurfaces in hyper-Kähler manifolds

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• 作者：Stefan Ivanov ; Ivan Minchev…
• 关键词：Quaternionic contact ; Hypersurfaces ; Hyper ; Kähler ; Quaternionic projective space ; 3 ; Sasaki
• 刊名：Annali di Matematica Pura ed Applicata (1923 -)
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：196
• 期：1
• 页码：245-267
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1618-1891
• 卷排序：196

文摘

We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space \(\mathbb {H}^{n+1}\) and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in \(\mathbb {H}^{n+1}\) is contained in one of the three qc-hyperquadrics in \(\mathbb {H}^{n+1}\). Moreover, we show that an embedded qc-hypersurface in a hyper-Kähler manifold is qc-conformal to a qc-Einstein space and the Riemannian curvature tensor of the ambient hyper-Kähler metric is degenerate along the hypersurface.