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

报告题目:Reductions of Gauss-Codazzi equations to the sixth Painlev\'e equation


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






摘要: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)





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