Instability of some Riemannian manifolds with real Killing spinors

2018/10/10 by Wang, Changliang, Wang, M. Y. -K. · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.04526

Abstract

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, l}=\rm SU(3)/i_{k, l}(S¹) (which are all nearly \rm G₂ except N_1,0), 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 Kähler ones (except \rm G₂/\rm SU(3)).

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