The reduction of symplectic structure and Sternberg construction

Anatol Odzijewicz

Displaying similar documents to “The reduction of symplectic structure and Sternberg construction”

Symplectic Killing spinors

Svatopluk Krýsl (2012)

Commentationes Mathematicae Universitatis Carolinae

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Let $(M, ω)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla$ . Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one...

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

Archivum Mathematicum

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Consider a flat symplectic manifold $(M^{2 l}, ω)$ , $l \geq 2$ , admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If $λ$ is an eigenvalue of the symplectic Dirac operator such that $- ı l λ$ is not a symplectic Killing number, then $\frac{l - 1}{l} λ$ is an eigenvalue of the symplectic Rarita-Schwinger operator.

Symplectic topology and hamiltonian dynamics

I. Ekeland, H. Hofer (1987-1988)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Toric structures on near-symplectic 4-manifolds

David T. Gay, Margaret Symington (2009)

Journal of the European Mathematical Society

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A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on...