Asymptotical flatness and cone structure at infinity

Anton Petrunin, Wilderich Tuschmann

Research output: Contribution to journalArticle

12 Scopus citations

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 ℝm-2 x S, where S is an asymptotically flat surface.

Original languageEnglish (US)
Pages (from-to)775-788
Number of pages14
JournalMathematische Annalen
Volume321
Issue number4
DOIs
StatePublished - Dec 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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