## Reductions of Gauss-Codazzi equations to the sixth Painlev'e equation

**Title**：Reductions of Gauss-Codazzi equations to the sixth Painlev\'e equation

**Speaker**：Prof. Robert Conte (\'Ecole normale sup\'erieure de Cachan, France)

**Date:** 16:00-17:00 pm; November 14; 2013

**Place**：Conference Room A404, Department of Mathematical Sciences

**Abstract****：**We first recall the Gauss-Codazzi equations, which govern the geometry of surfaces in R^n. In 1897, Hazzidakis found a reduction to a codimension-2 P6 equation in the case n=3, and our natural motivation is to find a reduction to the full (codimension-0) P6. Since the Gauss-Codazzi equations are underdetermined (three equations in four unknowns), we first restrict them to a determined system in order to compute its Lie point symmetries. This allows us to improve the result of Hazzidakis. (joint work with A. Michel Grundland)

**Contact**：Runliang Lin