Randers旋转2-回转球的割迹
The cut locus of a Randers rotational 2-sphere of revolution
摘要：
本文研究了Randers旋转2-旋转球$(M, F = α+β)$的割迹的结构。我们证明了当Randers曲面的高斯曲率沿子午线单调时，点$q\in M$的割迹是相对半弯子午线或对跖纬线的子弧上的点（定理1.1）.更一般地，在高斯曲率沿子午线不是单调的，但是赤道上的点$q$的割迹是同一赤道的子弧的情况下，不同于极点的任何点$\widetilde q\in M$的割迹是对极纬线的子弧（定理1.2）。最后给出了一些例子，并指出了与黎曼情形的一些不同之处。
英文摘要：
In the present paper we study the structure of the cut locus of a Randers rotational 2-sphere of revolution $(M, F = α+β)$. We show that in the case when the Gaussian curvature of the Randers surface is monotone along a meridian, the cut locus of a point $q\in M$ is a point on a subarc of the opposite half bending meridian or of the antipodal parallel (Theorem 1.1). More generally, in the case when the Gaussian curvature is not monotone along the meridian, but the cut locus of a point $q$ on the equator is a subarc of the same equator, the cut locus of any point $\widetilde q\in M$ different from poles is a subarc of the antipodal parallel (Theorem 1.2). Some examples are also given at the last section and some differences with the Riemannian case are pointed out.
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