Local splitting theorems for riemannian manifolds

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2 Scopus citations


In this paper we establish two local versions of the Cheeger-Gromoll Splitting Theorem. We show that if a complete Riemannian manifold M has nonnegative Ricci curvature outside a compact set B and contains a line γ which does not intersect B, then the line splits in a maximal neighborhood that is contained in M \ B. We use this result to give a simplified proof that M has a bounded number of ends. We also prove that if M has sectional curvature which is nonnegative (and bounded from above) in a tubular neighborhood U of a geodesic γ which is a line in U, then U splits along γ.

Original languageEnglish (US)
Pages (from-to)1231-1239
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Apr 1994


  • Asymptotic ray
  • Line
  • Ricci curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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