Complete manifolds with nonnegative Ricci curvature and quadratically nonnegatively curved infinity. (English) Zbl 0901.53023

Let \(M\) be a complete, noncompact Riemannian manifold. For any \(r>0\), let \(K_p(r):=\inf K\) on \(M\setminus B_r(p)\), where \(B_r(p)\) is the geodesic ball of radius \(r\) around \(p\in M\), \(k\) denotes the sectional curvature of \(M\), and the infimum is taken over all the sections at all points on \(M\setminus B_r(p)\).
The authors suppose \(M\) with nonnegative Ricci curvature and \(K_p(r)\geq-C/(1+r^2)\) for some constant \(C>0\). They obtain some topological finiteness theorems for \(M\) satisfying above conditions and some additional conditions on the volume growth.


53C20 Global Riemannian geometry, including pinching
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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