Publication details
Quaternionic contact hypersurfaces in hyper-Kähler manifolds
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Annali di Matematica Pura ed Applicata |
| MU Faculty or unit | |
| Citation | |
| web | http://link.springer.com/article/10.1007/s10231-016-0571-x/fulltext.html |
| Doi | https://doi.org/10.1007/s10231-016-0571-x |
| Field | General mathematics |
| Keywords | Quaternionic contact; Hypersurfaces; Hyper-Kahler; Quaternionic projective space; 3-Sasaki |
| Description | We describe explicitly all quaternionic contact hypersurfaces (qc-hypersurfaces) in the flat quaternion space Hn+1 and the quaternion projective space. We show that up to a quaternionic affine transformation a qc-hypersurface in Hn+1 is contained in one of the three qc-hyperquadrics in Hn+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. |
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