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arXiv · 1301.0447

Formal conserved quantities for isothermic surfaces

F. E. Burstall·S. D. Santos
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Abstract

Isothermic surfaces in $S^n$ are characterised by the existence of a pencil $\nabla^t$ of flat connections. Such a surface is special of type $d$ if there is a family $p(t)$ of $\nabla^t$-parallel sections whose dependence on the spectral parameter $t$ is polynomial of degree $d$. We prove that any isothermic surface admits a family of $\nabla^t$-parallel sections which is a formal Laurent series in $t$. As an application, we give conformally invariant conditions for an isothermic surface in $S^3$ to be special.

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F. E. Burstall, S. D. Santos. 2013-01-03. Formal conserved quantities for isothermic surfaces. https://doi.org/10.1007/s10711-013-9915-5

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