完备Riemann流形之测地线

Geodesics in a Complete Riemann Manifold

讨论了完备R iem ann流形上测地线上的共轭点的存在性与几何性质,证明了截面.γ∧v的曲率k(.γ∧v)≥0的完备测地线:γ(-∞,+∞)→M为共轭点测地线的充要条件是k(.γ∧v)=0.

The paper discusses the existence and geometric properties of conjugate points of the geodesics in a complete Riemarmian manifold, and proves that for a complete geodesic γ：（-∞,＋∞）→M, if k（γ∧ν）≥0then γ is a geodesic without conjugate points if and only ifk（γ∧ν） = 0.