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Non-umbilical quaternionic contact hypersurfaces in hyper-Kähler manifolds. (English) Zbl 1430.53062

Summary: It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler manifold is qc-conformal to a qc-Einstein structure which is locally qc-equivalent to the 3-Sasakian sphere, the quaternionic Heisenberg group or the hyperboloid.

MSC:

53C40 Global submanifolds
53C56 Other complex differential geometry
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