Killing spinors and hypersurfaces (Q6597298)

The authors consider a pseudo-Riemannian spin manifold \(Z\) of signature \((p,q+1)\) (resp., \((p,q+1)\)) with \(p+q=n\) odd. They show that the existence of a Killing spinor on \(Z\) to an oriented hypersurface of signature \((p,q)\) gives rise to a couple of spinor fields satisfying differential equations of order \(1\). They call these spinors harmful structures. Conversely, they show later that any given real analytic pseudo-Riemannian spin manifold \(M\) with a harmful structure allows to embed the manifold in a pseudo-Riemannian Einstein manifold carrying a Killing spinor.