On the geometry of asymptotically flat manifolds
On the geometry of asymptotically flat manifolds
复制标题
渐近平坦流形的几何
作者：
Xiuxiong Chen;Yu Li
本文研究了具有控制完整性的渐近平坦流形的几何性质。我们证明了这样的流形的任何一端承认一个ALE流形上的精化环面纤维化。此外，我们证明了一个Hitchin-Thorpe不等式定向Ricci平坦的$4$-流形曲率衰减和控制holonomy。作为应用，我们证明了在一个同胚于$mathbb R ^4 $的$4$-流形上的任何完备渐近平坦Ricci平坦度量必等距于欧氏度量或Taub-NUT度量，只要无穷远点的切锥不是$mathbb R imes mathbb R_+$.
In this paper, we investigate the geometry of asymptotically flat manifolds with controlled holonomy. We show that any end of such manifold admits a refined torus fibration over an ALE manifold. In addition, we prove a Hitchin-Thorpe inequality for oriented Ricci-flat $4$-manifolds with curvature decay and controlled holonomy. As an application, we show that any complete asymptotically flat Ricci-flat metric on a $4$-manifold which is homeomorphic to $mathbb R^4$ must be isometric to the Euclidean or the Taub-NUT metric, provided that the tangent cone at infinity is not $mathbb R imes mathbb R_+$.
DOI：
10.1515/9781400859306
发表时间：
1988
期刊：
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影响因子：
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作者：
M. Atiyah;N. Hitchin
通讯作者：
M. Atiyah;N. Hitchin