Some properties of tangent Dirac structures of higher order

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

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


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