Integration of the Gauss-Codazzi equations

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Abstract

The Gauss-Codazzi equations imposed on the elements of the first and the second quadratic forms of a surface embedded in ℝ3 are integrable by the dressing method. This method allows constructing classes of Combescure-equivalent surfaces with the same "rotation coefficients." Each equivalence class is defined by a function of two variables ("master function of a surface"). Each class of Combescure-equivalent surfaces includes the sphere. Different classes of surfaces define different systems of orthogonal coordinates of the sphere. The simplest class (with the master function zero) corresponds to the standard spherical coordinates.

Original languageEnglish (US)
Pages (from-to)946-956
Number of pages11
JournalTheoretical and Mathematical Physics
Volume128
Issue number1
DOIs
StatePublished - Jul 1 2001

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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