论文标题
奇异空间中的周期性测量学
Periodic geodesics in singular spaces
论文作者
论文摘要
我们将Lyusternik和FET的经典结果扩展到了封闭的大地测量学上的奇异空间。我们表明，如果某些固定的$κ> 0 $和$π_n（x）\ ne（x）\ ne 0 $，对于某些$ n> 0 $ n> 0 $，那么$ x $，如果$ x $是满足CAT（$κ$）条件的紧凑地测量公制空间（$κ$）条件，则$ n> $ x $具有定期的测量。例如，当地猫（$κ$）歧管满足了这种情况。我们的结果更普遍地适用于紧凑型局部独特的大地测量空间。
We extend the classical result of Lyusternik and Fet on the existence of closed geodesics to singular spaces. We show that if $X$ is a compact geodesic metric space satisfying the CAT($κ$) condition for some fixed $κ>0$ and $π_n(X)\ne 0$ for some $n>0$ then $X$ has a periodic geodesic. This condition is satisfied for example by locally CAT($κ$) manifolds. Our result applies more generally to compact locally uniquely geodesic spaces.
