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Canonical Poisson-Nijenhuis structures on higher order tangent bundles

P. M. Kouotchop Wamba (2014)

Annales Polonici Mathematici

Let M be a smooth manifold of dimension m>0, and denote by S c a n the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and Π T the complete lift of Π on TM. In a previous paper, we have shown that ( T M , Π T , S c a n ) is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to T r M have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on T A M are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002), 243-257],...

Some properties of tangent Dirac structures of higher order

P. M. Kouotchop Wamba, A. Ntyam, J. Wouafo Kamga (2012)

Archivum Mathematicum

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...

Tangent Dirac structures of higher order

P. M. Kouotchop Wamba, A. Ntyam, J. Wouafo Kamga (2011)

Archivum Mathematicum

Let L be an almost Dirac structure on a manifold M . In [2] Theodore James Courant defines the tangent lifting of L on T M 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.

Tangent lifts of higher order of multiplicative Dirac structures

P. M. Kouotchop Wamba, A. Ntyam (2013)

Archivum Mathematicum

The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac structures...

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