Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Obata-type characterization of doubly-warped product K\''ahler
  manifolds   We give a characterization {\sl \`a la Obata} for certain families of
K\''ahler manifolds. These results are in the same line as other extensions of
the well-known Obata's rigidity theorem from \cite{Obata62}, like for instance
the generalizations in \cite{RanjSant97} and \cite{Santhanam07}. Moreover, we
give a complete description of the so-called K\''ahler doubly-warped product
structures whose underlying metric is Einstein.

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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc