Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypersymplectic structures with torsion on Lie algebroids   Hypersymplectic structures with torsion on Lie algebroids are investigated.
We show that each hypersymplectic structure with torsion on a Lie algebroid
determines three Nijenhuis morphisms. From a contravariant point of view, these
structures are twisted Poisson structures. We prove the existence of a
one-to-one correspondence between hypersymplectic structures with torsion and
hyperk\"{a}hler structures with torsion. We show that given a Lie algebroid
with a hypersymplectic structure with torsion, the deformation of the Lie
algebroid structure by any of the transition morphisms does not affect the
hypersymplectic structure with torsion. We also show that if a triplet of
$2$-forms is a hypersymplectic structure with torsion on a Lie algebroid $A$,
then the triplet of the inverse bivectors is a hypersymplectic structure with
torsion for a certain Lie algebroid structure on the dual $A^*$, and
conversely. Examples of hypersymplectic structures with torsion are included.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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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: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th