A construction of Courant algebroids on foliated manifolds

TL;DR

This paper presents a method to construct Courant algebroids on foliated manifolds by extending transversal-Courant algebroids with a specific decomposition of the tangent bundle.

Contribution

It introduces a new construction of Courant algebroids on foliated manifolds based on transversal-Courant algebroids and bundle decompositions.

Findings

Constructs Courant algebroids on foliated manifolds.

Provides a systematic way to extend transversal-Courant algebroids.

Enhances understanding of geometric structures on foliated spaces.

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 $T\mathcal{F}\oplus T^*\mathcal{F}\oplus E$.