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Twistor Operators in Symplectic Geometry

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Abstract

On a symplectic manifold equipped with a symplectic connection and a metaplectic structure, we define two families of sequences of differential operators, called the symplectic twistor operators. We prove that if the connection is torsion-free and Weyl-flat, the sequences in these families form complexes.

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  1. Mathematical Institute of Charles University, Sokolovská 49/83, 186 75 Praha 8, Karlín, Czechia

    Svatopluk Krýsl

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The author thanks for financial supports from the founding No. 20-11473S granted by the Czech Science Foundation and from the institutional support program “Progres Q47” granted by the Charles University.

This article is part of the Topical Collection on Proceedings ICCA 12, Hefei, 2020, edited by Guangbin Ren, Uwe Kahler, Rafał Abłamowicz, Fabrizio Colombo, Pierre Dechant, Jacques Helmstetter, G. Stacey Staples, Wei Wang.

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Krýsl, S. Twistor Operators in Symplectic Geometry. Adv. Appl. Clifford Algebras 32, 14 (2022). https://doi.org/10.1007/s00006-022-01199-y

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