Open Access
October 2009 Special symplectic connections
Michel Cahen, Lorenz J. Schwachhöfer
J. Differential Geom. 83(2): 229-271 (October 2009). DOI: 10.4310/jdg/1261495331


By a special symplectic connection we mean a torsion free connection which is either the Levi-Civita connection of a Bochner-Kähler 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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Michel Cahen. Lorenz J. Schwachhöfer. "Special symplectic connections." J. Differential Geom. 83 (2) 229 - 271, October 2009.


Published: October 2009
First available in Project Euclid: 22 December 2009

zbMATH: 1070.53050
MathSciNet: MR2577468
Digital Object Identifier: 10.4310/jdg/1261495331

Rights: Copyright © 2009 Lehigh University

Vol.83 • No. 2 • October 2009
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