Formal conserved quantities for isothermic surfaces

F. E. Burstall, S. D. Santos

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Abstract

Isothermic surfaces in Sn are characterised by the existence of a pencil  ∇t∇∇t of flat connections. Such a surface is special of type d if there is a family p t of ∇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 ∇t-parallel sections which is a formal Laurent series in t. As an application, we give conformally invariant conditions for an isothermic surface in S3 to be special.

Original languageEnglish
Pages (from-to)191-205
JournalGeometriae Dedicata
Volume172
Issue number1
DOIs
Publication statusPublished - Oct 2014

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