Special symplectic connections

Michel Cahen Universit´e Libre de Bruxelles L Schwachhöfer Technische Universit¨at Dortmund

Differential Geometry mathscidoc:1609.10139

Journal of Differential Geometry, 83, (2), 229-271, 2009
By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-K¨ahler metric of arbitrary signature, a Bochner-bi-Lagrangian connection, a connection of Ricci type or a connection with special symplectic holonomy. A manifold or orbifold with such a connection is called special symplectic. We show that the symplectic reduction of (an open cell of) a parabolic contact manifold by a symmetry vector field is special symplectic in a canonical way. Moreover, we show that any special symplectic manifold or orbifold is locally equivalent to one of these symplectic reductions. As a consequence, we are able to prove a number of global properties, including a classification in the compact simply connected case.
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  author={Michel Cahen, and L Schwachhöfer},
  booktitle={Journal of Differential Geometry},
Michel Cahen, and L Schwachhöfer. SPECIAL SYMPLECTIC CONNECTIONS . 2009. Vol. 83. In Journal of Differential Geometry. pp.229-271. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911201347890015796.
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