The geometric properties of the complete noncompact surface with nonnegative curvature
In this paper, the author proves that every geodesic \(r: [0, +\infty)\to M,\) where \(M\) is a simply connected surface with nonnegative curvature, goes to infinity. But this may be false if \(\dim (M) \geq 3\). Using this condition, the author also proves that for such a surface, its cut locus is nothing but its first conjugate locus.
scientific article; zbMATH DE number 1643535