Instability of some Riemannian manifolds with real Killing spinors

Changliang Wang; M. Y. -K. Wang

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arXiv · 1810.04526

Instability of some Riemannian manifolds with real Killing spinors

Changliang Wang·M. Y. -K. Wang

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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 $N_{k, l}={\rm SU}(3)/i_{k, l}(S^{1})$ (which are all nearly ${\rm G}_2$ 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 K\"ahler ones (except ${\rm G}_2/{\rm SU}(3)$).

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BibTeX RIS

Changliang Wang, M. Y. -K. Wang. 2018-10-10. Instability of some Riemannian manifolds with real Killing spinors. https://arxiv.org/abs/1810.04526

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