Symplectic curvatue tensors
type: Item
instance of: scholarly article
title: Symplectic curvatue tensors
zbMATH Open document ID: 0571.53025
DOI: 10.1007/BF01339231
author: Izu Vaisman
published in: Monatshefte für Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178256
review text: In this paper one gives the decomposition of the space of tensors which have the symmetries of the covariant curvature tensor of a torsionless symplectic connection into Sp(n)-irreducible components. This leads to three classes of symplectic connections: flat, Ricci flat and reducible (i.e., with an expression like for Kähler manifolds of constant holomorphic sectional curvature). These cases are discussed for the canonical symplectic connection of a pair of transversal polarizations, where corresponding characteristic properties are given. In the reducible case, the Pontrjagin classes of the manifold are computed. If the pair of polarizations is real, and it has singularities, the Lehmann residues are considered [\textit{D. Lehmann}, Ann. Inst. Fourier 31, No.1, 83-98 (1981; Zbl 0432.57007)].
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 3911211
zbMATH Keywords: curvature tensor
zbMATH Keywords: symplectic connections
zbMATH Keywords: transversal polarizations
zbMATH Keywords: Pontrjagin classes
zbMATH Keywords: Lehmann residues
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3911211