We prove that the systolic ratio of a sphere of revolution $S$ does not exceed $\pi$ and equals $\pi$ if and only if $S$ is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by shifting the tangent unit circles by a Killing vector field. We prove that in this class of metrics the systolic ratio does not exceed $\pi$ and equals $\pi$ if and only if the metric is Riemannian and Zoll.

中文翻译：

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黎曼和芬斯勒革命领域的急剧收缩不等式

我们证明旋转球体的收缩率 $S$ 不超过 $\pi$ 并且等于 $\pi$ 当且仅当 $S$ 是 Zoll。更一般地，我们考虑旋转球体上的旋转对称 Finsler 度量，其定义是通过使用 Killing 矢量场移动切线单位圆来定义的。我们证明，在此类度量中，当且仅当度量是黎曼和 Zoll 时，收缩率不超过 $\pi$ 并且等于 $\pi$。