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arXiv · 1609.02838

Non-umbilical quaternionic contact hypersurfaces in hyper-K\"ahler manifolds

Stefan Ivanov·Ivan Minchev·Dimiter Vassilev
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Abstract

We show that any compact quaternionic contact (qc) hypersurfaces in a hyper-K\"ahler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. We also show that any nowhere umbilical qc hypersurface in a hyper-K\"ahler manifold is endowed with an involutive 7-dimensional distribution whose integral leafs are locally qc-conformal to the standard 3-Sasakian sphere.

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Stefan Ivanov, Ivan Minchev, Dimiter Vassilev. 2016-09-09. Non-umbilical quaternionic contact hypersurfaces in hyper-K\"ahler manifolds. https://arxiv.org/abs/1609.02838

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