Curvature at infinity of open nonnegatively curved manifolds
Let \(\Sigma\) be a soul of a complete open Riemannian manifold of nonnegative sectional curvature. Let \(\kappa\) (t) be the maximum of the curvature at all points of M with the distance \(\geq t\) from \(\Sigma\). The authors obtain a bound on the decay of the function \(\kappa\) under suitable topological conditions. Among others, if \(n=\dim M\) is odd, \(k=\dim \Sigma\), \(\alpha =2-2k/(n-1)\) and \(\chi\) (M)\(\neq 0\), then either lim sup \(\kappa\) (t)t\({}^{\alpha}>0\) or M is a flat Euclidean space.
scientific article; zbMATH DE number 4111490