# Formal conserved quantities for isothermic surfaces

Authors
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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