无焦点测地线

The Geodesics Without Focal Points

从测地线的共轭点、焦点的定义出发,证明了对任意具正曲率的完备二维Gauss曲面,γ:[0,+∞)→M为测地线,则存在t>0,γ(t)是γ(0)之焦点.从而说明了焦点与共轭点的差异,并对这种差异性进行了较深入的讨论.

By the definitions of the conjugate point and the focal point in a geodesic,the paper proves that for any geodesic γ:［0,+∞)→M,in a complete Gauss surface M with positive curvature,there exists t＞0 such that γ(t) is a focal point of γ(0).This fact reflects the difference between the focal point and the conjugate point.Moreover,the paper discusses this difference thoroughly.