### Abstract

An overview of the various transformations of isothermic surfaces and their interrelations is given using aquaternionic formalism. Applications to the theory of cmc-1 surfaces inhyperbolic space are given and relations between the two theories are discussed. Within this context, we give Möbius geometric characterizations for cmc-1 surfaces in hyperbolic space and theirminimal cousins.

Original language | English |
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Pages (from-to) | 185-205 |

Number of pages | 21 |

Journal | Annals of Global Analysis and Geometry |

Volume | 19 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 |

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## Cite this

Hertrich-Jeromin, U., Musso, E., & Nicolodi, L. (2001). Möbius geometry of surfaces of constant mean curvature 1 in hyperbolic space.

*Annals of Global Analysis and Geometry*,*19*(2), 185-205. https://doi.org/10.1023/A:1010738712475