Sequences of Levy Transformations and Multi-Wro\'nski Determinant Solutions of the Darboux System
dg-ga
2009-10-30 v1 Differential Geometry
Exactly Solvable and Integrable Systems
solv-int
Abstract
Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multi-Wro\'nski determinants. These formulae are for the tangent vectors, Lam\`e coefficients, rotation coefficients and points of the surface.
Keywords
Cite
@article{arxiv.dg-ga/9707013,
title = {Sequences of Levy Transformations and Multi-Wro\'nski Determinant Solutions of the Darboux System},
author = {Q. P. Liu and Manuel Mañas},
journal= {arXiv preprint arXiv:dg-ga/9707013},
year = {2009}
}
Comments
9 pages, LaTeX2e using Babel and AMS-LaTex packages