{"id":{"repo_id":"unf","oai_identifier":"oai:digitalcommons.unf.edu:etd-1552"},"canonical_url":"https://search.dev.ndltd.org/etd/unf/oai:digitalcommons.unf.edu:etd-1552","repository":{"repo_id":"unf","name":"University of North Florida","base_url":"https://digitalcommons.unf.edu/do/oai/"},"display":{"title":"Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs","abstract":"Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each surface and provide examples of each transition.","abstract_html":"Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each surface and provide examples of each transition.","abstract_has_math":false,"creators":["Olsen, William Edward"],"institution":"UNF Digital Commons","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T05:21:49Z","subjects":["Thesis; University of North Florida; UNF; Dissertations; Academic -- UNF -- Master of Science in Mathematical Science; Dissertations; Academic -- UNF -- Mathematics","Geometry and Topology","Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.unf.edu/etd/521","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Olsen, William Edward"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-01-01T08:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["UNF Digital Commons"]},{"key":"dc:type","label":"Dc Type","values":["thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Thesis; University of North Florida; UNF; Dissertations; Academic -- UNF -- Master of Science in Mathematical Science; Dissertations; Academic -- UNF -- Mathematics","Geometry and Topology","Mathematics","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.unf.edu/etd/521","https://digitalcommons.unf.edu/context/etd/article/1552/viewcontent/ETD1192PAC.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each surface and provide examples of each transition."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:source","label":"Dc Source","values":["UNF Graduate Theses and Dissertations"]},{"key":"dc:title","label":"Title","values":["Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs"]}]}],"canonical_facts":{"dc:creator":["Olsen, William Edward"],"dc:date":["2014-01-01T08:00:00Z"],"dc:description":["Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each surface and provide examples of each transition."],"dc:format":["application/pdf"],"dc:identifier":["https://digitalcommons.unf.edu/etd/521","https://digitalcommons.unf.edu/context/etd/article/1552/viewcontent/ETD1192PAC.pdf"],"dc:publisher":["UNF Digital Commons"],"dc:source":["UNF Graduate Theses and Dissertations"],"dc:subject":["Thesis; University of North Florida; UNF; Dissertations; Academic -- UNF -- Master of Science in Mathematical Science; Dissertations; Academic -- UNF -- Mathematics","Geometry and Topology","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs"],"dc:type":["thesis"]},"updated_at":"2026-07-24T05:21:49Z"}