Transitive Courant algebroids

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We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal, Whitney sum E ⊕ C where E is a given Courant algebroid and C is a flat, pseudo-Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive Courant algebroid, that is, a Courant algebroid with a surjective anchor, and describe a class of transitive Courant algebroids which are Whitney sums of a Courant subalgebroid with neutral metric and Courant-like bracket and a pseudo-Euclidean vector bundle with a flat, metric connection. In particular, this class contains all the transitive Courant algebroids of minimal rank; for these, the flat term mentioned above is zero. The results extend to regular Courant algebroids, that is, Courant algebroids with a constant rank anchor. The paper ends with miscellaneous remarks and an appendix on Dirac linear spaces.

Original languageEnglish
Pages (from-to)1737-1758
Number of pages22
JournalInternational Journal of Mathematics and Mathematical Sciences
Issue number11
StatePublished - 31 Jul 2005

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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