Reductions of Gauss-Codazzi equations
Differential Geometry
2017-10-16 v1 Exactly Solvable and Integrable Systems
Abstract
We prove that conformally parametrized surfaces in Euclidean space of curvature admit a symmetry reduction of their Gauss-Codazzi equations whose general solution is expressed with the sixth Painlev\'e 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.
Cite
@article{arxiv.1601.04300,
title = {Reductions of Gauss-Codazzi equations},
author = {Robert Conte and A. Michel Grundland},
journal= {arXiv preprint arXiv:1601.04300},
year = {2017}
}
Comments
25 pages, to appear, Studies in applied mathematics