Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms

Details Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms Darboux transformations for twisted so(p,q) system and local isometric immersion of space forms

1998-08-17

arxiv.org/abs/solv-int/9808006v1

Inverse Problems 14 (1998) 1353-1370

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 21 pages, 5 Postscript figures, to appear in Inverse Problems (1998)

Scientific paper

10.1088/0266-5611/14/5/018

For the n-dimensional integrable system with a twisted so(p,q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms with flat normal bundle and linearly independent curvature normals to give the explicit expression of the position vector. Some examples are given from the trivial solutions and standard imbedding T^n\to R^{2n}.

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