关于无共轭点的黎曼柱面的平坦性
On the flatness of Riemannian cylinders without conjugate points
摘要：
没有共轭点的完备黎曼2-柱面是平坦的，有什么适当的几何条件？具有非正曲率的例子表明，必须假定圆柱的两端是次线性地张开的。我们表明，亚线性增长的两端确实是足够的，如果它是由horocycles的长度来衡量。这是用来推广结果K。Burns和G.”[9]，《易经》云：“君子之道，在于仁。Koehler [18]，其中末端的开口是根据最短的不可收缩环来测量的。
英文摘要：
What are appropriate geometric conditions ensuring that a complete Riemannian 2-cylinder without conjugate points is flat? Examples with nonpositive curvature show that one has to assume that the ends of the cylinder open sublinearly. We show that sublinear growth of the ends is indeed sufficient if it is measured by the length of horocycles. This is used to extend results by K. Burns and G. Knieper [9], and by H. Koehler [18], where the opening of the ends is measured in terms of shortest noncontractible loops.
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