Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds
2017 ◽
Vol 2019
(18)
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pp. 5649-5673
Keyword(s):
Abstract 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.
2006 ◽
Vol 17
(01)
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pp. 35-43
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1998 ◽
Vol 21
(1)
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pp. 69-72
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2016 ◽
Vol 08
(04)
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pp. 589-626
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1995 ◽
Vol 18
(2)
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pp. 331-340
2014 ◽
Vol 150
(11)
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pp. 1869-1902
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1989 ◽
Vol 114
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pp. 77-122
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