Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson--K\"ahler fibration I: curvature of the base manifold   We start from a finite dimensional Higgs bundle description of a result of
Burns on negative curvature property of the space of complex structures, then
we apply the corresponding infinite dimensional Higgs bundle picture and obtain
a precise curvature formula of a Weil--Petersson type metric for general
relative K\"ahler fibrations. In particular, our curvature formula implies a
Burns type negative curvature property of the base manifold for a special class
of maximal variation K\"ahler fibrations (named Poisson--K\"ahler fibrations).

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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga