# Some properties of tangent Dirac structures of higher order

## P. M. Kouotchop Wamba, A. Ntyam, and J. Wouafo Kamga

Address:

Department of Mathematics, The University of Yaoundé 1, P.O BOX, 812, Yaoundé, Cameroon

Department of Mathematics, ENS Yaounde, P.O BOX 47, Yaoundé, Cameroon

E-mail:

wambapm@yahoo.fr

wouafoka@yahoo.fr

antyam@uy1-uninet.cm

Abstract: 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 $L^{r}$.

AMSclassification: primary 53C15; secondary 53C75, 53D05.

Keywords: Dirac structure, prolongations of vector fields, prolongations of differential forms, Dirac structure of higher order, natural transformations.

DOI: 10.5817/AM2012-3-233