We investigate the distribution of lengths of closed geodesics on complete and simply connected Sasakian space forms of dimension greater than 1. When its constant ϕ-sectional curvature k is irrational and satisfies $k>-9/4$ or $k<-4$, we can see that two closed geodesics on this manifold are congruent to each other in strong sense by an isometry of this manifold if and only if they have a common length. When k is rational and $k\ne -3,1$, the number of congruence classes of closed geodesics of given length is finite, but not uniformly finite, and its growth order with respect to their lengths is less than polynomial order.

中文翻译：

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完全简单连接的Sasakian空间形式的长度谱

我们研究尺寸大于1的完整且简单连接的Sasakian空间形式上闭合测地线的长度分布。当其恒定ϕ截面曲率k不合理且满足时$ķ>-9/4$ 要么 $ķ<-4$，我们可以看到，该流形上的两个闭合测地线在且仅当它们具有相同的长度时，通过该流形的等轴测图在强意义上彼此一致。当k是有理数且$ķ\ne -3，\mathrm{1个}$，给定长度的闭合测地线的全等类的数量是有限的，但不是均匀有限的，并且其相对于其长度的增长顺序小于多项式顺序。