Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of some Riemannian manifolds with real Killing spinors   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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The categories of this paper are: cs
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The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph