Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine surfaces which are K\"ahler, para-K\"ahler, or nilpotent K\"ahler   Motivated by the construction of Bach flat neutral signature Riemannian
extensions, we study the space of parallel trace free tensors of type $(1,1)$
on an affine surface. It is shown that the existence of such a parallel tensor
field is characterized by the recurrence of the symmetric part of the Ricci
tensor.

5
The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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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: chao-dyn