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 Yaoundé, P.O BOX, 47 Yaoundé, Cameroon
Department of Mathematics, The University of Yaoundé 1, P.O BOX, 812, Yaoundé Cameroon

E-mail:
wambapm@yahoo.fr
antyam@uy1-uninet.cm
wouafoka@yahoo.fr

Abstract: 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.

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

Keywords: Dirac structure, almost Dirac structure, tangent functor of higher order, natural transformations.