Local splitting theorems for riemannian manifolds

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume120
Issue number4
DOIs
StatePublished - 1994

Fingerprint

Riemannian Manifold
Line
Theorem
Nonnegative Curvature
Ricci Curvature
Sectional Curvature
Intersect
Compact Set
Geodesic
Non-negative

Keywords

  • Asymptotic ray
  • Line
  • Ricci curvature

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Local splitting theorems for riemannian manifolds. / Cai, MingLiang; Galloway, Gregory J; Liu, Z.

In: Proceedings of the American Mathematical Society, Vol. 120, No. 4, 1994, p. 1231-1239.

Research output: Contribution to journalArticle

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