Non-umbilical quaternionic contact hypersurfaces in hyper-K\"ahler   manifolds
  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. 
Stefan Ivanov, Ivan Minchev, Dimiter Vassilev
math.DG