Dirac structures for generalized Courant and Courant algebroids

Abstract

We establish some fundamental relations between Dirac subbundles $L$ for the generalized Courant algebroid $(A\oplus A^{\ast },\varphi +W)$ over a differentiable manifold $M$ and the associated Dirac subbubndles $\tilde{L}$ for the corresponding Courant algebroid $\tilde{A}\oplus {\tilde{A}}^{\ast }$ over $M\times \mathbb{R}$.

To appear in proceedings of the conference Poisson 2004