Local splitting theorems for Riemannian manifolds
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- by M. Cai, G. J. Galloway and Z. Liu PDF
- Proc. Amer. Math. Soc. 120 (1994), 1231-1239 Request permission
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 $\gamma$ which does not intersect $B$, then the line splits in a maximal neighborhood that is contained in $\overline {M\backslash B}$. 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 $\gamma$ which is a line in $U$, then $U$ splits along $\gamma$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1231-1239
- MSC: Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1994-1186984-2
- MathSciNet review: 1186984