## Abstract

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 language | English |
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Pages (from-to) | 1737-1758 |

Number of pages | 22 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2005 |

Issue number | 11 |

DOIs | |

State | Published - 31 Jul 2005 |

## ASJC Scopus subject areas

- Mathematics (miscellaneous)