Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yamabe problem for Gauss-Bonnet curvatures: a local result around
  space forms   It is shown in the paper "Variational Properties of the Gauss-Bonnet
Curvatures" of M.L. Labbi, that metrics with constant 2k-Gauss-Bonnet curvature
on a closed n-dimensional manifold, 1<2k<n, are critical points for a certain
Hilbert type functional with respect to volume preserving conformal variations.
This motivates the corresponding Yamabe problem: is it true that any metric on
a closed manifold is conformal to a metric with constant 2k-Gauss-Bonnet
curvature? Using perturbative methods we affirmatively answer this question for
small perturbations of certain space forms. More precisely, if (X,g) is a
non-flat closed space form not isometric to a round sphere, we show the
existence of a neighborhood U, of g, in the space of metrics such that any g'
in U is conformal to a metric whose 2k-Gauss-Bonnet curvature is constant.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: nlin