• DOI:10.1007/978-3-540-33421-7_2
• Corpus ID: 10448303

Symplectic connections

@inproceedings{Bieliavsky2005SymplecticC,
  title={Symplectic connections},
  author={Pierre Bieliavsky and Michel Cahen and Simone Gutt and John Howard Rawnsley and Lorenz J. Schwachhofer},
  year={2005}
}

• P. Bieliavsky, M. Cahen, +2 authors L. Schwachhofer
• Published 8 November 2005
• Mathematics

This article is an overview of the results obtained in recent years on symplectic connections. We present what is known about preferred connections (critical points of a variational principle). The class of Ricci-type connections (for which the curvature is entirely determined by the Ricci tensor) is described in detail, as well as its far reaching generalization to special connections. A twistorial construction shows a relation between Ricci-type connections and complex geometry. We give a construction of Ricci-flat symplectic connections. We end up by presenting, through an explicit example, an approach to noncommutative symplectic symmetric spaces.