Author's School

Graduate School of Arts & Sciences

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.

DOI

https://doi.org/10.7936/K7DR2SKF

Comments

Permanent URL: http://dx.doi.org/10.7936/K7DR2SKF

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