具非负曲率完备非紧曲面的几何性质

The Geometric Properties of the Complete Noncompact Surface with Nonnegative Curvature

本文证明了单连通完备非紧具非负曲率之曲面的任一测地线γ：［０，＋∞）→Ｍ均趋于∞处这一几何性质，指出了一般的高维流形不具有此性质．本文还证明了单连通完备非紧具非负曲率的曲面的割迹与第一共轭轭迹是一致的；并且讨论了一般高维流形的共轭点与测地线的关系．

For a simply connected open surface with nonnegative curvature, we prove that every geodesic γ: [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 dis- cuss the relation between the conjugate points and the geodesic, in an n-dimensional Rieman- nian manifold.