Vol. 231, No. 1, 2007

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 276: 1  2
Vol. 275: 1  2
Vol. 274: 1  2
Vol. 273: 1  2
Vol. 272: 1  2
Vol. 271: 1  2
Vol. 270: 1  2
Vol. 269: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
On Ahlfors’ Schwarzian derivative and knots

Martin Chuaqui

Vol. 231 (2007), No. 1, 51–61
Abstract

We extend Ahlfors’ definition of the Schwarzian derivative for curves in euclidean space to include curves on arbitrary manifolds, and give applications to the classical spaces of constant curvature. We also derive in terms of the Schwarzian a sharp criterion for a closed curve in 3 to be unknotted.

Keywords
Schwarzian derivative, simple curve, conformal metric, knot
Mathematical Subject Classification 2000
Primary: 53A04, 53A30
Secondary: 53A55
Milestones
Received: 26 December 2005
Revised: 5 September 2006
Accepted: 19 September 2006
Published: 1 May 2007
Authors
Martin Chuaqui
Facultad de Matemáticas
P. Universidad Católica de Chile
Casilla 306
Santiago 22
Chile
www.mat.puc.cl