Special Symplectic Connections

Michel Cahen; Lorenz J. Schwachhöfer

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Special Symplectic Connections

Michel Cahen·Lorenz J. Schwachhöfer

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Abstract

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. 2009-09-11. Special Symplectic Connections. https://arxiv.org/abs/math/0402221

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