标题： 在有效圆作用下不变的超辛结构 显示英文标题

标题： Hypersymplectic Structures Invariant Under an Effective Circle Action

摘要： 在4流形上的超辛结构是一个三元组的辛形式，其中任何非零线性组合再次是辛的。 在2006年， Donaldson猜想在紧致4流形上任何超辛结构都可以通过同调的超辛结构变形为一个超凯勒三元组。 我们在初始结构在有效的$S^1$-作用下不变的假设下证明了这一点。 特别是我们表明底流形微分同胚于$\mathbb{T}^4$。 显示英文摘要

摘要： A hypersymplectic structure on a 4-manifold is a triple of symplectic forms for which any non-zero linear combination is again symplectic. In 2006, Donaldson conjectured that on a compact 4-manifold any hypersymplectic structure can be deformed through cohomologous hypersymplectic structures to a hyperk\"ahler triple. We prove this under the assumption that the initial structure is invariant under an effective $S^1$-action. In particular we show that the underlying 4-manifold is diffeomorphic to $\mathbb{T}^4$.