On Ahlfors' Schwarzian derivative and knots

被引：3

作者：

Chuaqui, Martin ^{[1
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Math, Santiago 22, Chile

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2007年 / 231卷 / 01期

关键词：

Schwarzian derivative; simple curve; conformal metric; knot;

D O I：

10.2140/pjm.2007.231.51

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 R-3 to be unknotted.

引用

页码：51 / 61

页数：11

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