A generalization of the Cheeger-Gromoll splitting theorem
The original theorem of \textit{J. Cheeger} and \textit{D. Gromoll} [J. Differ. Geom. 6, 119-128 (1971; Zbl 0223.53033)] states that a complete connected Riemannian manifold M splits isometrically as a product \({\mathbb{R}}\times M'\) if the Ricci curvature of M is nonnegative and M contains a line. In the present paper, the curvature assumption is weakened to an average version, namely that along each ray \(\sigma\) the limes inferior of \(\int^{t}_{0}Ric(\sigma '(s),\sigma '(s))ds\) for \(t\to \infty\) is nonnegative. The essential point is the subharmonicity of Busemann functions under the given curvature condition.
scientific article; zbMATH DE number 3994460