{"id":{"repo_id":"wustl","oai_identifier":"oai:openscholarship.wustl.edu:etd-1088"},"canonical_url":"https://search.dev.ndltd.org/etd/wustl/oai:openscholarship.wustl.edu:etd-1088","repository":{"repo_id":"wustl","name":"Washington University in St. Louis","base_url":"https://openscholarship.wustl.edu/do/oai/"},"display":{"title":"Equivariant Deformations of Horospherical Surfaces","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Deutsch, Michael"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Gary Jensen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T06:12:48Z","subjects":["Mathematics","Physics","Elementary Particles and High Energy","CMC1","Goursat","horospherical","minimal","surface","transform"],"languages":["English (en)"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7DR2SKF"],"render_values":[{"text":"https://doi.org/10.7936/K7DR2SKF","href":"https://doi.org/10.7936/K7DR2SKF","code":true}]}]},"links":{"outbound_url":"https://openscholarship.wustl.edu/etd/89","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Gary Jensen"]},{"key":"dc:creator","label":"Author","values":["Deutsch, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2010-01-01T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Physics","Elementary Particles and High Energy","CMC1","Goursat","horospherical","minimal","surface","transform"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English (en)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://openscholarship.wustl.edu/etd/89"]},{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.7936/K7DR2SKF"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Equivariant Deformations of Horospherical Surfaces"]}]}],"canonical_facts":{"dc:contributor":["Gary Jensen"],"dc:creator":["Deutsch, Michael"],"dc:date.available":["2010-01-01T08:00:00Z"],"dc:description.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."],"dc:identifier":["https://openscholarship.wustl.edu/etd/89"],"dc:identifier.doi":["https://doi.org/10.7936/K7DR2SKF"],"dc:language":["English (en)"],"dc:subject":["Mathematics","Physics","Elementary Particles and High Energy","CMC1","Goursat","horospherical","minimal","surface","transform"],"dc:title":["Equivariant Deformations of Horospherical Surfaces"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T06:12:48Z"}