On Ahlfors’ Schwarzian derivative and knots
On Ahlfors’ Schwarzian derivative and knots
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 ޒ 3 to be unknotted.