Geodesic
Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus
Documenta mathematica, Tome 2 (1997), pp. 335-350
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A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. It introduces a rich algebraic structure and allows the use of global frames while, at the same time, incorporates the classical “geometric” model of Möbius geometry providing geometric clarity. This way, it provides the foundation for the development of new techniques in Möbius differential geometry.
DOI : 10.4171/dm/33
Classification : 53A10, 53C42
Mots-clés : isothermic surface, Darboux transformation, Christoffel transformation, constant mean curvature, Goursat transformation, curved flat, Weierstrass representation 
@article{10_4171_dm_33,
     author = {Udo Hertrich-Jeromin},
     title = {Supplement on curved flats in the space of point pairs and isothermic surfaces: {A} quaternionic calculus},
     journal = {Documenta mathematica},
     pages = {335--350},
     year = {1997},
     volume = {2},
     doi = {10.4171/dm/33},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/33/}
}
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Udo Hertrich-Jeromin. Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus. Documenta mathematica, Tome 2 (1997), pp. 335-350. doi: 10.4171/dm/33

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