# 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} }

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…

## 60 Citations

### Remarks on Symplectic Connections

- Mathematics
- 2006

This note contains a short survey on some recent work on symplectic connections: properties and models for symplectic connections whose curvature is determined by the Ricci tensor, and a procedure to…

### Connections on contact manifolds and contact twistor space

- Mathematics
- 2010

In this paper we generalize the definition of symplectic connection to the contact case. It turns out that any odd-dimensional manifold equipped with a contact form admits contact connections and…

### Symplectic connections induced by the Chern connection

- Mathematics
- 2008

Let (M;!) be a symplectic manifold and F be a Finsler struc- ture on M. In the present paper we deflne a lift of the symplectic two-form ! on the manifold TMn0, and flnd the conditions that the Chern…

### Critical symplectic connections on surfaces

- MathematicsJournal of Symplectic Geometry
- 2019

The space of symplectic connections on a symplectic manifold is a symplectic affine space. M. Cahen and S. Gutt showed that the action of the group of Hamiltonian diffeomorphisms on this space is…

### Remarks on symplectic twistor spaces

- Mathematics
- 2009

We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study self-holomorphic sections of the general twistor…

### Symmetries of the Space of Linear Symplectic Connections

- Mathematics
- 2017

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment…

### Extremal symplectic connections on surfaces

- Mathematics
- 2014

M. Cahen and S. Gutt found the moment map for the action of the symplectomorphism group on the symplectic affine space of symplectic connections on a symplectic manifold. This paper studies extremal…

### On a Connection Used in Deformation Quantization

- Mathematics
- 2020

Using natural lifting operations, we give a coordinate-free proof of the fact that the connection used by Bordemann, Neumaier and Waldmann to construct the Fedosov standard ordered star product on…

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