Prescribing the behaviour of geodesics in negative curvature

Details Prescribing the behaviour of geodesics in negative curvature Prescribing the behaviour of geodesics in negative curvature

2007-06-18

arxiv.org/abs/0706.2579v1

Mathematics

Differential Geometry

89 pages

Scientific paper

Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big enough) penetration in one of them, and otherwise avoid (or do not enter too much in) them. Several applications are given, including a definite improvement of the unclouding problem of [PP1], the prescription of heights of geodesic lines in a finite volume such M, or of spiraling times around a closed geodesic in a closed such M. We also prove that the Hall ray phenomenon described by Hall in special arithmetic situations and by Schmidt-Sheingorn for hyperbolic surfaces is in fact only a negative curvature property.

Affiliated with

Also associated with

No associations

Rating

Prescribing the behaviour of geodesics in negative curvature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Prescribing the behaviour of geodesics in negative curvature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Prescribing the behaviour of geodesics in negative curvature will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-609818