Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs
William E. Olsen · University of North Florida Digital Commons (University of North Florida) · 2014
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.