Dirac structures for generalized Courant and Courant algebroids

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We establish some fundamental relations between Dirac subbundles $L$ for the generalized Courant algebroid $(A\oplus A^{\ast}, ϕ+W)$ over a differentiable manifold $M$ and the associated Dirac subbubndles $\tilde{L}$ for the corresponding Courant algebroid $\tilde{A} \oplus \tilde{A}^{\ast}$ over $M\times \R$.
To appear in proceedings of the conference Poisson 2004

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