Ivanov, Stefan; Minchev, Ivan; Vassilev, Dimiter Non-umbilical quaternionic contact hypersurfaces in hyper-Kähler manifolds. (English) Zbl 1430.53062 Int. Math. Res. Not. 2019, No. 18, 5649-5673 (2019). 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 Keywords:induced quaternionic contact structure; 3-Sasakian sphere; quaternionic Heisenberg group PDFBibTeX XMLCite \textit{S. Ivanov} et al., Int. Math. Res. Not. 2019, No. 18, 5649--5673 (2019; Zbl 1430.53062) Full Text: DOI arXiv