The Schwarzian derivative and Euler--Lagrange equations

Wojciech Kryński

doi:10.1016/j.geomphys.2022.104665

paper

The Schwarzian derivative and Euler--Lagrange equations

arXiv:2112.08712 · doi:10.1016/j.geomphys.2022.104665

Abstract

We study the Schwarzian derivative from a variational viewpoint. Firstly we show that the Schwarzian derivative defines a first integral of the Euler--Lagrange equation of a second order Lagrangian. Secondly, we show that the Schwarzian derivative itself is the Euler--Lagrange operator for an appropriately chosen class of variations.