Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally symmetric submanifolds lift to spectral manifolds   In this work we prove that every locally symmetric smooth submanifold gives
rise to a naturally defined smooth submanifold of the space of symmetric
matrices, called spectral manifold, consisting of all matrices whose ordered
vector of eigenvalues belongs to the locally symmetric manifold. We also
present an explicit formula for the dimension of the spectral manifold in terms
of the dimension and the intrinsic properties of the locally symmetric
manifold.

9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
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: solv-int
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con