Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein connections with skew-torsion on Berger spheres   The invariant metric affine connections on Berger spheres which are Einstein
with skew torsion are determined in both Riemannian and Lorentzian signature.
Expressions of such connections are explicitly given. In particular, every
Berger sphere with Lorentzian signature admits invariant metric affine
connections Einstein with skew-torsion up to $\mathbb{S}^3$. For Riemannian
signature, the existence of such connections strongly depends on the dimension
of the sphere and on the scale of the deformation used for the Berger metric.
In particular, there are Riemaniann Berger spheres, not Einstein, which admit
invariant metric affine connections Einstein with skew-torsion.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci