SU(3)-structures on hypersurfaces of manifolds with G_2-structure
  We study SU(3)-structures induced on orientable hypersurfaces of seven-dimensional manifolds with G_2-structure. Taking Gray-Hervella types for both structures into account, we relate the type of SU(3)-structure and the type of G_2-structure with the shape tensor of the hypersurface. Additionaly, we show how to compute the intrinsic SU(3)-torsion and the intrinsic G_2-torsion by means of exterior algebra. 
Francisco Martin Cabrera