The Geometric Properties of the Complete Noncompact Surface with Nonnegative Curvature

Abstract:

      For a simply connected open surface with nonnegative curvature, we prove that every geodesicγ:[0, +∞)→ Mgoes to infinity, its cut locus is just the same as its first con jugate locus. But all above characters are not true for a manifold with dim≥3. We also discuss the relation between the conjugate points and the geodesic, in an n-dimensional Riemannian manifold.