Trisymplectic manifolds

A trisymplectic structure on a complex $2n$-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has rank $2n$, $n$ or $0$. We show that a trisymplectic manifold is equipped with a holomorphic $3$-web and the Chern connection of this $3$-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkaehler manifold. We show that the moduli space $M$ of holomorphic vector bundles on ${\mathbb{CP}}^3$ that are trivial along a line admits a trisymplectic structure.