English

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