Let (Mn, o) be a pointed open complete manifold with Ricci curvature bounded from below by and nonnegative outside the ball B(o, a). It has recently been shown that there is an upper bound for the number of ends of such a manifold which depends only on Aa and the dimension 71 of the manifold M". We will give a gap theorem in this paper which shows that there exists an such that M" has at most two ends We also give examples to show that, in dimension n > 4, such manifolds in general do not carry any complete metric with nonnegative Ricci Curvature for any.
ASJC Scopus subject areas
- Applied Mathematics