Hyperbolic 3-manifolds with nonintersecting closed geodesics
A complete (orientable) Riemannian manifold is said to have the spd-property if all its closed geodesics are simple and pairwise disjoint. In the paper under review, the spd-property is investigated for Riemannian \(3\)-manifolds which admit a geometrically finite hyperbolic structure. The authors prove that either the generic hyperbolic structure has the spd-property or no hyperbolic structure has it, and show that both situations occur. They analyze the case when the manifold is the interior of a handlebody or of the product of a surface with an interval of negative Euler characteristic and proof that, for these manifolds, the generic hyperbolic structure has the spd-property. Finally it is observed that having the spd-property is a commensurability invariant.
scientific article; zbMATH DE number 1960053