Local splitting theorems for Riemannian manifolds

Authors:
M. Cai, G. J. Galloway and Z. Liu

Journal:
Proc. Amer. Math. Soc. **120** (1994), 1231-1239

MSC:
Primary 53C20

MathSciNet review:
1186984

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

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DOI:
https://doi.org/10.1090/S0002-9939-1994-1186984-2

Keywords:
Ricci curvature,
line,
asymptotic ray

Article copyright:
© Copyright 1994
American Mathematical Society