Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The second Dirac eigenvalue of a nearly parallel $G_2$-manifold   We investigate the second Dirac eigenvalue on Riemannian manifolds admitting
a Killing spinor. In small dimensions the whole Dirac spectrum depends on
special eigenvalues on functions and 1-forms. We compute and discuss the
formulas in dimension $n = 7$.

30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat