Symplectic Killing spinors. (English) Zbl 1249.53093

Summary: Let \((M,\omega )\) 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 may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere \(S^2\) equipped with the volume form of the round metric.


53D05 Symplectic manifolds (general theory)
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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