Complex of twistor operators in symplectic spin geometry
| Autor: | Svatopluk Krýsl |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Mathematics - Differential Geometry
Spin geometry Weyl tensor Pure mathematics General Mathematics Metaplectic structure Affine connection Connection (mathematics) Twistor theory symbols.namesake Differential Geometry (math.DG) Mathematics - Symplectic Geometry FOS: Mathematics symbols Symplectic Geometry (math.SG) 53C07 53D05 58J10 Mathematics::Differential Geometry Mathematics::Symplectic Geometry Symplectic manifold Mathematics Symplectic geometry |
| Zdroj: | Monatshefte für Mathematik. 161:381-398 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-009-0158-3 |
| Popis: | For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but one of these operators are of first order. The first order ones are symplectic analogues of the twistor operators known from Riemannian spin geometry. We prove that under the condition the symplectic Weyl curvature tensor field of the symplectic connection vanishes, the mentioned sequence forms a complex. This gives rise to a new complex for the so called Ricci type symplectic manifolds, which admit a metaplectic structure. 18 pages, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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