Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System

Details Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System Sequences of Levy Transformations and Multi-Wroński Determinant Solutions of the Darboux System

1997-07-21

arxiv.org/abs/dg-ga/9707013v1

Mathematics

Differential Geometry

9 pages, LaTeX2e using Babel and AMS-LaTex packages

Scientific paper

10.1016/S0393-0440(97)00074-0

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.

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