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On
the geometry of asymptotically flat manifolds
Xiuxiong Chen and Yu Li |
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Geometry & Topology 25 (2021) 2469–2572
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Abstract |
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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 –manifolds with curvature decay and controlled holonomy. As an application, we show that any complete, asymptotically flat, Ricci-flat metric on a –manifold which is homeomorphic to must be isometric to the Euclidean or the Taub–NUT metric, provided that the tangent cone at infinity is not . |
Keywords
asymptotically flat, collapsing, torus fiber bundle
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Mathematical Subject Classification 2010
Primary: 53C20, 53C21, 53C23, 53C25, 53C29
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References |
Publication
Received: 4 December 2019
Revised: 27 July 2020
Accepted: 28 August 2020
Published: 3 September 2021
Proposed: John Lott
Seconded: Mark Gross, Simon Donaldson
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Authors |
| Xiuxiong Chen | |
| Institute of Geometry and
Physics University of Science and Technology of China Hefei China |
Mathematics Department Stony Brook University Stony Brook, NY United States |
| Yu Li | |
| Institute of Geometry and
Physics University of Science and Technology of China Hefei China |
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