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2021 On the geometry of asymptotically flat manifolds
Xiuxiong Chen, Yu Li
Geom. Topol. 25(5): 2469-2572 (2021). DOI: 10.2140/gt.2021.25.2469

Abstract

We investigate the geometry of asymptotically flat manifolds with controlled holonomy. We show that any end of such manifold admits a torus fibration over an ALE end. 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 4 must be isometric to the Euclidean or the Taub–NUT metric, provided that the tangent cone at infinity is not ×+.

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Xiuxiong Chen. Yu Li. "On the geometry of asymptotically flat manifolds." Geom. Topol. 25 (5) 2469 - 2572, 2021. https://doi.org/10.2140/gt.2021.25.2469

Information

Received: 4 December 2019; Revised: 27 July 2020; Accepted: 28 August 2020; Published: 2021
First available in Project Euclid: 12 October 2021

Digital Object Identifier: 10.2140/gt.2021.25.2469

Subjects:
Primary: 53C20, 53C21, 53C23, 53C25, 53C29

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.25 • No. 5 • 2021
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