Small curvature surfaces in hyperbolic 3-manifolds

Details Small curvature surfaces in hyperbolic 3-manifolds Small curvature surfaces in hyperbolic 3-manifolds

2004-09-23

arxiv.org/abs/math/0409455v1

Mathematics

Geometric Topology

28 pages, 8 figures. See also http://www.math.columbia.edu/~clein/papers.html

Scientific paper

In a paper of Menasco and Reid, it is conjectured that there exist no hyperbolic knots in S^3 for which the complement contains a closed embedded totally geodesic surface. In this note, we show that one can get "as close as possible" to a counter-example. Specifically, we construct a sequence of hyperbolic knots {K_n} with complements containing closed embedded essential surfaces having principal curvatures converging to zero as n tends to infinity. We also construct a family of two-component links for which the complements contain closed embedded totally geodesic surfaces of arbitrarily large genera. In addition, we prove that a closed embedded surface with sufficiently small principal curvatures is not only quasi-Fuchsian (a result of W. Thurston's), but it is also either acylindrical or else the boundary of a twisted I-bundle.

Affiliated with

Also associated with

No associations

Rating

Small curvature surfaces in hyperbolic 3-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 Small curvature surfaces in hyperbolic 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small curvature surfaces in hyperbolic 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77844