Reductions of Gauss-Codazzi equations
arXiv:1601.04300 · doi:10.1111/sapm.12121
Abstract
We prove that conformally parametrized surfaces in Euclidean space $\Rcubec$ of curvature admit a symmetry reduction of their Gauss-Codazzi equations whose general solution is expressed with the sixth Painlevé function. Moreover, it is shown that the two known solutions of this type (Bonnet 1867, Bobenko, Eitner and Kitaev 1997) can be recovered by such a reduction.
25 pages, to appear, Studies in applied mathematics