Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyper-ParaHermitian manifolds with torsion   Necessary and sufficient conditions for the existence of a
hyper-parahermitian connection with totally skew-symmetric torsion
(HPKT-structure) are presented. It is shown that any HPKT-structure is locally
generated by a real (potential) function. An invariant first order differential
operator is defined on any almost hyper-paracomplex manifold showing that it is
two-step nilpotent exactly when the almost hyper-paracomplex structure is
integrable. A local HPKT-potential is expressed in terms of this operator.
Examples of (locally) invariant HPKT-structures with closed as well as
non-closed torsion 3-form on a class of (locally) homogeneous hyperparacomplex
manifolds (some of them compact) are constructed.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con