# Classification of integrable Weingarten surfaces possessing an \mathfrak{sl} (2)-valued zero curvature representation

@article{Baran2010ClassificationOI, title={Classification of integrable Weingarten surfaces possessing an \mathfrak\{sl\} (2)-valued zero curvature representation}, author={H. Baran and M. Marvan}, journal={Nonlinearity}, year={2010}, volume={23}, pages={2577-2597} }

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an (2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the… Expand

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