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arXiv · 1406.4256

Quaternionic contact hypersurfaces in hyper-K\"ahler manifolds

Stefan Ivanov·Ivan Minchev·Dimiter Vassilev
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Abstract

We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space $\Hnn$ and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in $\Hnn$ is contained in one of the three qc-hyperquadrics in $\Hnn$. Moreover, we show that an embedded qc-hypersurface in a hyper-K\"ahler manifold is qc-conformal to a qc-Einstein space and the Riemannian curvature tensor of the ambient hyper-K\"ahler metric is degenerate along the hypersurface.

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Stefan Ivanov, Ivan Minchev, Dimiter Vassilev. 2014-06-17. Quaternionic contact hypersurfaces in hyper-K\"ahler manifolds. https://arxiv.org/abs/1406.4256

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