Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of Hopf vector fields on Lorentzian Berger spheres   In this work, we study the stability of Hopf vector fields on Lorentzian
Berger spheres as critical points of the energy, the volume and the generalized
energy. In order to do so, we construct a family of vector fields using the
simultaneous eigenfunctions of the Laplacian and of the vertical Laplacian of
the sphere. The Hessians of the functionals are negative when they act on these
particular vector fields and then Hopf vector fields are unstable. Moreover, we
use this technique to study some of the open problems in the Riemannian case.

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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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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: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph