Supplement on Curved flats in the space of point pairs and Isothermic surfaces: A Quaternionic Calculus
Abstract
A quaternionic calculus for surface pairs in the conformal 4sphere 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 3space is given.
 Publication:

eprint arXiv:dgga/9709019
 Pub Date:
 September 1997
 DOI:
 10.48550/arXiv.dgga/9709019
 arXiv:
 arXiv:dgga/9709019
 Bibcode:
 1997dg.ga.....9019H
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 14 pages, Plain TeX