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 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.
- Publication:
-
eprint arXiv:dg-ga/9709019
- Pub Date:
- September 1997
- DOI:
- 10.48550/arXiv.dg-ga/9709019
- arXiv:
- arXiv:dg-ga/9709019
- Bibcode:
- 1997dg.ga.....9019H
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 14 pages, Plain TeX