Author's Department/Program
Mathematics
Language
English (en)
Date of Award
January 2010
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Chair and Committee
Gary Jensen
Abstract
The classical Goursat transform for minimal surfaces is interpreted as conformal transformation of the Gauss map, allowing us to "bend" these surfaces for certain geometric purposes. A simple analogue of this deformation is defined for CMC1 surfaces which makes the Goursat transform equivariant with respect to the Lawson correspondence, thereby increasing the number of explicitly computable examples of minimal/CMC1 cousin pairs. We then indicate how the Goursat transformation law and integrability conditions for the "spin curve" of a horospherical surface are analogous to the Lorentz transformation law and equations of motion for the wavefunction of a massless fermion.
Recommended Citation
Deutsch, Michael, "Equivariant Deformations of Horospherical Surfaces" (2010). All Theses and Dissertations (ETDs). 89.
https://openscholarship.wustl.edu/etd/89
Comments
Permanent URL: http://dx.doi.org/10.7936/K7DR2SKF