Some properties of tangent Dirac structures of higher order. (English) Zbl 1274.53052

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

Arch. Math., Brno 48, No. 3, 233-241 (2012).

An almost Dirac structure on a manifold \(M\) is a subbundle \(L\) of the vector bundle \(TM\oplus T^{\ast }M\) which is maximally isotropic under the symmetric pairing. A classical result is that \(L\) is integrable if and only if it corresponds to a Lie algebroid. The authors present an intrisic construction of tangent Dirac structures of higher order denoted by \(L^r\) and study some properties of \(L^r\). Special attention is paid to the Lie algebroid and the presymplectic foliation induced by \(L^r\).

Reviewer: Ivan Kolář (Brno)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C75	Geometric orders, order geometry
53D05	Symplectic manifolds (general theory)

Keywords:

Dirac structure; prolongations of vector fields; prolongations of differential forms; Dirac structure of higher order; natural transformation