A construction of Courant algebroids on foliated manifolds

Abstract

For any transversal-Courant algebroid $E$ on a foliated manifold $(M,\mathcal{F})$, and for any choice of a decomposition $TM=T\mathcal{F}\oplus Q$, we construct a Courant algebroid structure on $T\mathcal{F}\oplus T^*\mathcal{F}\oplus E$.