论文标题
在消失的曲率条件下，Riemannian扭曲空间的刚度结果
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
论文作者
论文摘要
在本文中，我们为四维的Riemannian歧管及其扭曲器空间提供了新的刚性结果。尤其是使用移动框架方法，我们证明$ \ mathbb {cp}^3 $是唯一的twistor空间，其Bochner张量是平行的；此外，我们对Hermitian Ricci并行和局部对称的扭曲器空间进行了分类，并显示了共同平坦的扭曲器空间的不存在。由于阿蒂亚，希钦和歌手，我们还概括了结果，这是关于里曼尼亚人四人的自以为是的。
In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathbb{CP}^3$ is the only twistor space whose Bochner tensor is parallel; moreover, we classify Hermitian Ricci-parallel and locally symmetric twistor spaces and we show the nonexistence of conformally flat twistor spaces. We also generalize a result due to Atiyah, Hitchin and Singer concerning the self-duality of a Riemannian four-manifold.
