Small curvature surfaces in hyperbolic 3-manifolds
| dc.creator | Leininger, Christopher J. | |
| dc.date | 2004-09-23 | |
| dc.date.accessioned | 2026-07-07T05:12:31Z | |
| dc.date.available | 2026-07-07T05:12:31Z | |
| dc.description | 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. | |
| dc.description | 28 pages, 8 figures. See also http://www.math.columbia.edu/~clein/papers.html | |
| dc.identifier | https://arxiv.org/abs/math/0409455 | |
| dc.identifier | http://arxiv.org/abs/math/0409455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72601 | |
| dc.subject | Geometric Topology | |
| dc.subject | Differential Geometry | |
| dc.subject | 57M50; 57M25; 53C42 | |
| dc.title | Small curvature surfaces in hyperbolic 3-manifolds | |
| dc.type | text |