On invariants of almost symplectic connections

Abstract

We study the irreducible decomposition under Sp(2n, 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.

References in corpus (1)

• Twistor theory of symplectic manifolds

Cited by in corpus (2)

• Differential geometry of ${\mathsf{SO}}^{\ast }(2n)$-type structures -- Integrability
• Differential geometry of ${\mathsf{SO}}^{\ast }(2n)$-type structures