Udo Hertrich-Jeromin, Emilio Musso, Lorenzo Nicolodi
Published 1998-10-28Version 1
Various transformations of isothermic surfaces are discussed and their interrelations are analyzed. Applications to cmc-1 surfaces in hyperbolic space and their minimal cousins in Euclidean space are presented: the Umehara-Yamada perturbation, the classical and Bryant's Weierstrass type representations, and the duality for cmc-1 surfaces are interpreted in terms of transformations of isothermic surfaces. A new Weierstrass type representation is introduced and a Moebius geometric characterization of cmc-1 surfaces in hyperbolic space and minimal surfaces in Euclidean space is given.
Comments: 18 pages, plain TeX, 8 PostScript figures
Journal: Ann. Global Anal. Appl. 19, 185-205 (2001)
On the index of constant mean curvature 1 surfaces in hyperbolic space
$δ$(3)-ideal null 2-type hypersurfaces in Euclidean spaces
Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space
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