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SYMPLECTIC CONNECTIONS WITH A PARALLEL RICCI CURVATURE

Published online by Cambridge University Press:  10 December 2003

Charles Boubel
Charles Boubel
Affiliation:
Université de Grenoble I, Institut Fourier (UMR 5582), BP 74, 38402 Saint Martin d’Hères Cedex, France ([email protected])
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Abstract

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A symplectic connection on a symplectic manifold, unlike the Levi-Civita connection on a Riemannian manifold, is not unique. However, some spaces admit a canonical connection (symmetric symplectic spaces, Kähler manifolds, etc.); besides, some ‘preferred’ symplectic connections can be defined in some situations. These facts motivate a study of the symplectic connections, inducing a parallel Ricci tensor. This paper gives the possible forms of the Ricci curvature on such manifolds and gives a decomposition theorem (linked with the holonomy decomposition) for them.

AMS 2000 Mathematics subject classification: Primary 53B05; 53B30; 53B35; 53C25; 53C55

Keywords

affine connectionsymplectic connectionRicci curvatureHolonomy groupEinstein manifoldspseudo-Riemannian manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 3 , October 2003 , pp. 747 - 766
Copyright
Copyright © Edinburgh Mathematical Society 2003