Spiraling spectra of geodesic lines in negatively curved manifolds

Details Spiraling spectra of geodesic lines in negatively curved manifolds Spiraling spectra of geodesic lines in negatively curved manifolds

2008-06-11

arxiv.org/abs/0806.1857v2

Mathematics

Differential Geometry

Revised version. To appear in Math. Z

Scientific paper

Given a negatively curved geodesic metric space M, we study the asymptotic penetration behaviour of geodesic lines of M in small neighbourhoods of closed geodesics and of other compact convex subsets of M. We define a spiraling spectrum which gives precise information on the asymptotic spiraling lengths of geodesic lines around these objects. We prove analogs of the theorems of Dirichlet, Hall and Cusick in this context. As a consequence, we obtain Diophantine approximation results of real numbers, complex numbers, or elements of the Heisenberg group by irrational quadratic ones.

Affiliated with

Also associated with

No associations

Rating

Spiraling spectra of geodesic lines in negatively curved manifolds 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 Spiraling spectra of geodesic lines in negatively curved manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spiraling spectra of geodesic lines in negatively curved manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-265741