Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bergman-Calabi diastasis and K\"ahler metric of constant holomorphic
  sectional curvature   We prove that for a bounded domain in $\mathbb C^n$ with the Bergman metric
of constant holomorphic sectional curvature being biholomorphic to a ball is
equivalent to the hyperconvexity or the exhaustiveness of the Bergman-Calabi
diastasis. By finding its connection with the Bergman representative
coordinate, we give explicit formulas of the Bergman-Calabi diastasis and show
that it has bounded gradient. In particular, we prove that any bounded domain
whose Bergman metric has constant holomorphic sectional curvature is Lu
Qi-Keng. We also extend a theorem of Lu towards the incomplete situation and
characterize pseudoconvex domains that are biholomorphic to a ball possibly
less a relatively closed pluripolar set.

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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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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: nlin
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The categories of this paper are: funct-an