Conformal Schwarzian Derivatives and Differential Equations

Abstract

We investigate the fundamental system of equations in the theory of conformal geometry, whose coefficients are considered as the conformal Schwarzian derivative. The integrability condition of the system is obtained in a simple method, which allow us to find a natural geometric structure on the solution space. From the solution spaces, using this geometric structure, we get a transformation whose Schwarzian derivative is equal to the given coefficients of the equation.