Year
2014
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
First Advisor
Dr. Daniel Dreibelbis
Second Advisor
Dr. Ognjen Milatovic
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Jose Franco
Department Chair
Dr. Scott Hochwald
College Dean
Dr. Barbara Hetrick
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.
Suggested Citation
Olsen, William Edward, "Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs" (2014). UNF Graduate Theses and Dissertations. 521.
https://digitalcommons.unf.edu/etd/521