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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.