Displaying similar documents to “Symplectic torus bundles and group extensions.”

Liouville forms in a neighborhood of an isotropic embedding

Frank Loose (1997)

Annales de l'institut Fourier

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A Liouville form on a symplectic manifold ( X , ω ) is by definition a potential β of the symplectic form - d β = ω . Its center M is given by β - 1 ( 0 ) . A normal form for certain Liouville forms in a neighborhood of its center is given.

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 ≥ 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 l - 1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.