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On Invariants of Almost Symplectic Connections

  • R. Albuquerque
  • R. Picken
Article
  • 95 Downloads

Abstract

We study the irreducible decomposition under \(Sp(2n,{\mathbb R})\) of the space of torsion tensors of almost symplectic connections. Then a description of all symplectic quadratic invariants of torsion-like tensors is given. When applied to a manifold M with an almost symplectic structure, these instruments give preliminary insight for finding a preferred linear almost symplectic connection on M. We rediscover Ph. Tondeur’s Theorem on almost symplectic connections. Properties of torsion of the vectorial kind are deduced.

Keywords

Almost symplectic Linear connection Torsion Quadratic invariant. 

Mathematics Subject Classification (2010)

53A55 53B05 53D15 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Departamento de Matemática da Universidade de Évora and Centro de Investigação em Matemática e Aplicações (CIMA-UÉ)ÉvoraPortugal
  2. 2.Departamento de Matemática and CAMGSD - Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior TécnicoUniversity of LisbonLisboaPortugal

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