Mathematics – Differential Geometry
Scientific paper
1997-09-24
Doc. Math. J. DMV 2, 335-350 (1997)
Mathematics
Differential Geometry
14 pages, Plain TeX
Scientific paper
A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given.
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