Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nijenhuis structures on Courant algebroids   We study Nijenhuis structures on Courant algebroids in terms of the canonical
Poisson bracket on their symplectic realizations. We prove that the Nijenhuis
torsion of a skew-symmetric endomorphism N of a Courant algebroid is
skew-symmetric if the square of N is proportional to the identity, and only in
this case when the Courant algebroid is irreducible. We derive a necessary and
sufficient condition for a skew-symmetric endomorphism to give rise to a
deformed Courant structure. In the case of the double of a Lie bialgebroid
(A,A*), given an endomorphism n of A that defines a skew-symmetric endomorphism
N of the double of A, we prove that the torsion of N is the sum of the torsion
of n and that of the transpose of n.

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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph