Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrable geodesic flows and Multi-Centre versus Bianchi A metrics   It is shown that most, but not all, of the four dimensional metrics in the
Multi-Centre family with integrable geodesic flow may be recognized as
belonging to spatially homogeneous Bianchi type A metrics. We show that any
diagonal bi-axial Bianchi II metric has an integrable geodesic flow, and that
the simplest hyperk\"ahler metric in this family displays a finite dimensional
W-algebra for its observables. Our analysis puts also to light non-diagonal
Bianchi VI$_0$ and VII$_0$ metrics which seem to be new. We conclude by showing
that the elliptic coordinates advocated in the literature do not separate the
Hamilton-Jacobi equation for the tri-axial Bianchi IX metric.

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The categories of this paper are: cs
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
3
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: supr-con
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The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th