7-dimensional compact Riemannian manifolds with Killing spinors (Q756162)

Let M be a compact Riemannian spin manifold. A section \(\psi\) of the spin bundle is called a Killing spinor if \(\nabla_ X\psi =\lambda X\cdot \psi,\) where \(\lambda \neq 0\) is a (real) constant and X any tangent vector. The authors show that M has at least two independent Killing spinors if dim(M) is odd and M is simply connected and Einstein-Sasaki. In dimension 7 they classify (in a certain sense) the cases with two or three independent Killing or parallel spinors. Generalizations of these results have been obtained recently by \textit{Ch. Bär} (Preprint, Bonn 1991).