Some properties of tangent Dirac structures of higher order

summary:Let $M$ be a smooth manifold. The tangent lift of Dirac structure on $M$ was originally studied by T. Courant in [3]. The tangent lift of higher order of Dirac structure $L$ on $M$ has been studied in [10], where tangent Dirac structure of higher order are described locally. In this paper we give an intrinsic construction of tangent Dirac structure of higher order denoted by $L^{r}$ and we study some properties of this Dirac structure. In particular, we study the Lie algebroid and the presymplectic foliation induced by $L^{r}$

Tangent Dirac structures of higher order

summary:Let $L$ be an almost Dirac structure on a manifold $M$. In [2] Theodore James Courant defines the tangent lifting of $L$ on $TM$ and proves that: If $L$ is integrable then the tangent lift is also integrable. In this paper, we generalize this lifting to tangent bundle of higher order