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Integrable Flows for Starlike Curves in Centroaffine Space
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Integrable Flows for Starlike Curves in Centroaffine Space
Інший ID:
2010 Mathematics Subject Classification: 37K10; 53A20; 53C44
DOI: http://dx.doi.org/10.3842/SIGMA.2013.022
DOI: http://dx.doi.org/10.3842/SIGMA.2013.022
Посилання:
Integrable Flows for Starlike Curves in Centroaffine Space / A. Calini, T. Ivey, G.M. Beffa // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 30 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants
and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
The authors would like to acknowledge the careful and detailed work of the anonymous referees
in helping improve this paper. The authors also gratefully acknowledge support from the National Science Foundation: A. Calini through grants DMS-0608587 and DMS-1109017, and as
a current NSF employee; T. Ivey through grant DMS-0608587; and G. Mar´ı Bef fa through grant
DMS-0804541. T. Ivey also acknowledges support from the College of Charleston Mathematics
Department. G. Mar´ı Bef fa also acknowledges the support of the Simons Foundation through
their Fellows program.
Дата:
2013
Переглядів:
413
Завантажень:
225
Анотація:
We construct integrable hierarchies of flows for curves in centroaffine R³ through a natural pre-symplectic structure on the space of closed unparametrized starlike curves. We show that the induced evolution equations for the differential invariants are closely connected with the Boussinesq hierarchy, and prove that the restricted hierarchy of flows on curves that project to conics in RP² induces the Kaup-Kuperschmidt hierarchy at the curvature level.
