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Formal conserved quantities for isothermic surfaces

Authors
  • Burstall, F. E.
  • Santos, S. D.
Type
Published Article
Publication Date
Jan 03, 2013
Submission Date
Jan 03, 2013
Identifiers
DOI: 10.1007/s10711-013-9915-5
Source
arXiv
License
Yellow
External links

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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