Open AccessGeometric curve flows in low dimensional Cayley–Klein geometries
Author(s) -
Joseph Benson,
Francis Valiquette
Publication year - 2020
Publication title -
journal of integrable systems
Language(s) - English
Resource type - Journals
ISSN - 2058-5985
DOI - 10.1093/integr/xyaa003
Subject(s) - mathematics , curvature , equivariant map , integrable system , arc length , arc (geometry) , recursion (computer science) , mathematical analysis , geometry , pure mathematics , algorithm
Using the method of equivariant moving frames, we derive the evolution equations for the curvature invariants of arc-length parametrized curves under arc-length preserving geometric flows in two-, three- and four-dimensional Cayley–Klein geometries. In two and three dimensions, we obtain recursion operators, which show that the curvature evolution equations obtained are completely integrable.
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