Displaying similar documents to “Compact and small rank perturbations of conformally symplectic structures”

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 ∇ . 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 ≥ 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.

Symplectic spinor valued forms and invariant operators acting between them

Svatopluk Krýsl (2006)

Archivum Mathematicum

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Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.

Ellipticity of the symplectic twistor complex

Svatopluk Krýsl (2011)

Archivum Mathematicum

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For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections of certain infinite rank vector bundles defined over this manifold. The differential operators are symplectic analogues of the twistor operators known from Riemannian or Lorentzian spin geometry. It is known that the mentioned sequences form complexes if the...