Instability of some Riemannian manifolds with real Killing spinors

摘要

We prove the instability of some families of Riemannian manifolds with non-trivial real Killing spinors. These include the invariant Einstein metrics on the Aloff-Wallach spaces N-k,N-l = SU(3)/i(k,l)(S-1) (which are all nearly parallel G(2) except N-1,N-0), and Sasaki Einstein circle bundles over certain irreducible Hermitian symmetric spaces. We also prove the instability of most of the simply connected non-symmetric compact homogeneous Einstein spaces of dimensions 5, 6, and 7, including the strict nearly Kahler ones (except G(2)/SU(3)).