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Mathematische Annalen

, Volume 321, Issue 4, pp 775–788 | Cite as

Asymptotical flatness and cone structure at infinity

  • Anton Petrunin
  • Wilderich Tuschmann
Original article

Abstract.

We investigate asymptotically flat manifolds with cone structure at infinity. We show that any such manifold M has a finite number of ends, and we classify (except for the case dim M=4, where it remains open if one of the theoretically possible cones can actually arise) for simply connected ends all possible cones at infinity. This result yields in particular a complete classification of asymptotically flat manifolds with nonnegative curvature: The universal covering of an asymptotically flat m-manifold with nonnegative sectional curvature is isometric to \({\mathbb R}^{m-2}\times S\), whereS is an asymptotically flat surface.

Keywords

Manifold Finite Number Flat Surface Sectional Curvature Universal Covering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Anton Petrunin
    • 1
  • Wilderich Tuschmann
    • 2
  1. 1.Math. Dept. Pennsylvania State University, University Park, PA 16802, USA (e-mail: petrunin@math.psu.edu)US
  2. 2.Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse, D-04103 Leipzig, Germany (e-mail: tusch@mis.mpg.de)DE

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