论文标题
在Riemannian四曼鸟及其扭曲空间上：一个移动的框架方法
On Riemannian four-manifolds and their twistor spaces: a moving frame approach
论文作者
论文摘要
在本文中，我们使用移动框架方法，尤其是专注于爱因斯坦（Einstein）的非自身双重划分设置，研究了定向的riemannian四元式$ m $的扭曲空间$ z $。我们证明，$ z $几乎复杂的结构上的任何一般一阶线性条件都迫使基本歧管$ m $自我划，也恢复了大多数已知的相关刚度结果。因此，我们自然会导致考虑一阶二次条件，这表明爱因斯坦四个曼佛的Atiyah-hitchin-Singer几乎几乎是Hermitian Twistor空间，从适当的意义上讲，它与几乎是Kähler歧视的相似之处。
In this paper we study the twistor space $Z$ of an oriented Riemannian four-manifold $M$ using the moving frame approach, focusing, in particular, on the Einstein, non-self-dual setting. We prove that any general first-order linear condition on the almost complex structures of $Z$ forces the underlying manifold $M$ to be self-dual, also recovering most of the known related rigidity results. Thus, we are naturally lead to consider first-order quadratic conditions, showing that the Atiyah-Hitchin-Singer almost Hermitian twistor space of an Einstein four-manifold bears a resemblance, in a suitable sense, to a nearly Kähler manifold.
