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.
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Albuquerque, R., Picken, R. On Invariants of Almost Symplectic Connections. Math Phys Anal Geom 18, 8 (2015). https://doi.org/10.1007/s11040-015-9180-y
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DOI: https://doi.org/10.1007/s11040-015-9180-y