Integrable systems in projective differential geometry

E. V. Ferapontov

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Integrable systems in projective differential geometry

E. V. Ferapontov

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Abstract

Some of the most important classes of surfaces in projective 3-space are reviewed: these are isothermally asymptotic surfaces, projectively applicable surfaces, surfaces of Jonas, projectively minimal surfaces, etc. It is demonstrated that the corresponding projective "Gauss-Codazzi" equations reduce to integrable systems which are quite familiar from the modern soliton theory and coincide with the stationary flows in the Davey-Stewartson and Kadomtsev-Petviashvili hierarchies, equations of the Toda lattice, etc. The corresponding Lax pairs can be obtained by inserting a spectral parameter in the equations of the Wilczynski moving frame.

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E. V. Ferapontov. 1999-03-25. Integrable systems in projective differential geometry. https://arxiv.org/abs/math/9903150

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