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Minimal Immersions into the 3-Sphere and the Sinh-Gordon Equation

  • Sebastian Klein
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2229)

Abstract

We begin by describing the relationship between minimal immersions without umbilical points into the 3-sphere and solutions of the sinh-Gordon equation explicitly, especially to obtain the \(\mathfrak {sl}(2,\mathbb {C})\)-valued connection form αλ corresponding to the zero-curvature representation of the sinh-Gordon equation; from the integration of αλ we will obtain spectral data for periodic solutions of the sinh-Gordon equation.

References

  1. [Bo-2]
    A. Bobenko, Constant mean curvature surfaces and integrable equations. Usp. Mat. Nauk 46(4), 3–42 (1991)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Sebastian Klein
    • 1
  1. 1.School of Business Informatics & MathematicsUniversity of MannheimMannheimGermany

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