Dissertation
A new class of integrable surfaces related to Bertrand curves
Doctor of Philosophy (Ph.D.), Drexel University
Aug 2015
DOI:
https://doi.org/10.17918/etd-6667
Abstract
In this dissertation we present a new class of integrable surfaces related to Bertrand curves. These surfaces are foliations of constant-torsion curves and are generated by a particular geometric flow on constant-torsion curves. We see that the orbit of this flow traces out Bertrand curves on the surface. The surfaces discussed interpolate two known integrable systems and we establish the connection. We also use tools from soliton theory to generate surface solutions using Bäcklund transformations.
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Details
- Title
- A new class of integrable surfaces related to Bertrand curves
- Creators
- Jonah J. Smith - DU
- Contributors
- Ronald K. Perline (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- ix, 68 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 6667; 991014632380404721