Symplectic Killing spinors
Svatopluk Kr\'ysl

TL;DR
This paper investigates symplectic Killing spinor fields on symplectic manifolds with metaplectic structures, deriving a necessary zeroth order condition and computing explicit solutions for standard symplectic spaces and the sphere.
Contribution
It introduces a zeroth order necessary condition for symplectic Killing spinors and applies it to compute solutions on standard symplectic spaces and the sphere.
Findings
Derived a zeroth order necessary condition for symplectic Killing spinors.
Computed explicit symplectic Killing spinors on standard symplectic vector spaces.
Determined symplectic Killing spinors on the round sphere S^2.
Abstract
Let 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 topic of this paper. We derive a necessary condition satisfied by a symplectic Killing spinor field. The advantage of this condition consists in the fact that it is expressed by a zeroth order operator. This condition helps us substantionally to compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere equipped with the volume form of the round metric.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Geometric Analysis and Curvature Flows
