Special Symplectic Connections

Details Special Symplectic Connections Special Symplectic Connections

2004-02-13

arxiv.org/abs/math/0402221v3

Mathematics

Differential Geometry

35 pages, no figures. Exposition improved, some minor errors corrected. Version to be published by Jour.Diff.Geom

Scientific paper

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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