Date of Award
9-2009
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Franz Pedit
Second Advisor
Rob Kusner
Third Advisor
Peter Norman
Subject Categories
Mathematics
Abstract
The Grassmannian space GC(2, 4) embedded in CP5 as the Klein quadric of twistor theory has a natural interpretation in terms of the geometry of “round” 2-spheres in S4. The incidence of two lines in CP3 corresponds to the contact properties of two 2- spheres, where contact is generalized from tangency to include “half-tangency:” 2-spheres may be in contact at two isolated points. There is a connection between the contact properties of 2-spheres and soliton geometry through the classical Ribaucour and Darboux transformations. The transformation theory of surfaces in S4 is investigated using the recently developed theory of “Discrete Differential Geometry” with results leading to the conclusion that the discrete conformal maps into C of Hertrich-Jeromin, McIntosh, Norman and Pedit may be defined in terms a discrete integrable system employing halftangency in S4.
DOI
https://doi.org/10.7275/1079026
Recommended Citation
Shapiro, George, "On the Discrete Differential Geometry of Surfaces in S4" (2009). Open Access Dissertations. 135.
https://doi.org/10.7275/1079026
https://scholarworks.umass.edu/open_access_dissertations/135