Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs

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.

Grantor dc:publisher

UNF Digital Commons

Year dc:date

2014

Author dc:creator

• Olsen, William Edward

• 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

Repository record dc:identifier

https://digitalcommons.unf.edu/etd/521

OAI identifier oai:identifier

oai:digitalcommons.unf.edu:etd-1552