Generalized polarized manifolds.

Azzouz Awane

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On the geometry of the standard $k$ -symplectic and Poisson manifolds.

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Geometric prequantization of a generalized mechanical system.

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A new geometrical framework for time-dependent Hamiltonian mechanics.

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Connections on $k$ -symplectic manifolds.

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Geometric structures on spaces of weighted submanifolds.

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Some results for generalized cochains.

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Contact Homology, Capacity and Non-Squeezing in $ℝ^{2 n} \times S^{1}$ via Generating Functions

Sheila Sandon (2011)

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Starting from the work of Bhupal we extend to the contact case the Viterbo capacity and Traynor’s construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.

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Sergyeyev, Artur (2007)

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Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

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Differential forms on the Fréchet manifold $ℱ (S, M)$ of smooth functions on a compact $k$ -dimensional manifold $S$ can be obtained in a natural way from pairs of differential forms on $M$ and $S$ by the hat pairing. Special cases are the transgression map $Ω^{p} (M) \to Ω^{p - k} (ℱ (S, M))$ (hat pairing with a constant function) and the bar map $Ω^{p} (M) \to Ω^{p} (ℱ (S, M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].