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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...

The geography of simply-connected symplectic manifolds

Mi Sung Cho, Yong Seung Cho (2003)

Czechoslovak Mathematical Journal

By using the Seiberg-Witten invariant we show that the region under the Noether line in the lattice domain × is covered by minimal, simply connected, symplectic 4-manifolds.

The geometry of a closed form

Marisa Fernández, Raúl Ibáñez, Manuel de León (1998)

Banach Center Publications

It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on G 2 -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.

The infinitesimal counterpart of tangent presymplectic groupoids of higher order

P.M. Kouotchop Wamba, A. MBA (2018)

Archivum Mathematicum

Let G , ω be a presymplectic groupoid. In this paper we characterize the infinitesimal counter part of the tangent presymplectic groupoid of higher order, ( T r G , ω c ) where T r G is the tangent groupoid of higher order and ω c is the complete lift of higher order of presymplectic form ω .

The level crossing problem in semi-classical analysis. II. The Hermitian case

Yves Colin de Verdière (2004)

Annales de l’institut Fourier

This paper is the second part of the paper ``The level crossing problem in semi-classical analysis I. The symmetric case''(Annales de l'Institut Fourier in honor of Frédéric Pham). We consider here the case where the dispersion matrix is complex Hermitian.

The Lie groupoid analogue of a symplectic Lie group

David N. Pham (2021)

Archivum Mathematicum

A symplectic Lie group is a Lie group with a left-invariant symplectic form. Its Lie algebra structure is that of a quasi-Frobenius Lie algebra. In this note, we identify the groupoid analogue of a symplectic Lie group. We call the aforementioned structure a t -symplectic Lie groupoid; the “ t " is motivated by the fact that each target fiber of a t -symplectic Lie groupoid is a symplectic manifold. For a Lie groupoid 𝒢 M , we show that there is a one-to-one correspondence between quasi-Frobenius Lie algebroid...

Three results on the regularity of the curves that are invariant by an exact symplectic twist map

M.-C. Arnaud (2009)

Publications Mathématiques de l'IHÉS

A theorem due to G. D. Birkhoff states that every essential curve which is invariant under a symplectic twist map of the annulus is the graph of a Lipschitz map. We prove: if the graph of a Lipschitz map h:T→R is invariant under a symplectic twist map, then h is a little bit more regular than simply Lipschitz (Theorem 1); we deduce that there exists a Lipschitz map h:T→R whose graph is invariant under no symplectic twist map (Corollary 2).Assuming that the dynamic of a twist map restricted to a...

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