Integrable systems in projective differential geometry
Differential Geometry
2007-05-23 v1
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.
Cite
@article{arxiv.math/9903150,
title = {Integrable systems in projective differential geometry},
author = {E. V. Ferapontov},
journal= {arXiv preprint arXiv:math/9903150},
year = {2007}
}