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 α λ corresponding to the zero-curvature representation of the sinh-Gordon equation; from the integration of α λ we will obtain spectral data for periodic solutions of the sinh-Gordon equation.
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References
A. Bobenko, Constant mean curvature surfaces and integrable equations. Usp. Mat. Nauk 46(4), 3–42 (1991)
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Klein, S. (2018). Minimal Immersions into the 3-Sphere and the Sinh-Gordon Equation. In: A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation. Lecture Notes in Mathematics, vol 2229. Springer, Cham. https://doi.org/10.1007/978-3-030-01276-2_2
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DOI: https://doi.org/10.1007/978-3-030-01276-2_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01275-5
Online ISBN: 978-3-030-01276-2
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