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

Sha, Jiping; Shen, Zhongmin

Am. J. Math. 119, No. 6, 1399-1404 (1997).

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.

Reviewer: S.Ianus (Bucureşti)

MSC:

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

Keywords:

sectional curvature; Ricci curvature; Busemann function; topological finiteness; volume growth