Asymptotically flat manifolds and cone structure at infinity

Anton Petrunin and Wilderich Tuschmann

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Submission date: 06. Jul. 1999 (revised version: September 2001)
Pages: 13
published in: Mathematische Annalen, 321 (2001) 4, p. 775-788 
DOI number (of the published article): 10.1007/s002080100252
Bibtex
with the following different title: Asymptotical flatness and cone structure at infinity
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Abstract:
Let M be an asymptotically flat m-manifold which has cone structure at infinity. We show that M has a finite number of ends and classify for simply connected ends all possible cones at infinity (except for dim M=4 where it is not clear if one of the theoretically possible cones can actually arise). This leads in particular to a classification of asymptotically flat nonnegatively curved manifolds: The universal covering of an asymptotically flat m-manifold with nonnegative sectional curvature is isometric to R^m-2 x M², where M² is an asymptotically flat surface.