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A new class of integrable surfaces related to Bertrand curves
Dissertation   Open access

A new class of integrable surfaces related to Bertrand curves

Jonah J. Smith
Doctor of Philosophy (Ph.D.), Drexel University
Aug 2015
DOI:
https://doi.org/10.17918/etd-6667
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Abstract

Foliations (Mathematics) Torsion theory (Algebra) Mathematics
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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