Recurrent Geodesics in Flat Lorentz $3$-Manifolds

[摘要] Let $M$ be a complete flat Lorentz $3$-manifold $M$ with purelyhyperbolic holonomy $Gamma$. Recurrent geodesic rays are completelyclassified when $Gamma$ is cyclic. This implies that for any pair ofperiodic geodesics $gamma_1$, $gamma_2$, a unique geodesic forwardspirals towards $gamma_1$ and backward spirals towards $gamma_2$.

[学科分类] 数学（综合）

[关键词] geometric structures on low-dimensional manifolds;notions of recurrence