### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 048, 11 pages      arXiv:1310.1688      https://doi.org/10.3842/SIGMA.2014.048

### Multi-Hamiltonian Structures on Spaces of Closed Equicentroaffine Plane Curves Associated to Higher KdV Flows

Atsushi Fujioka a and Takashi Kurose b
a) Department of Mathematics, Kansai University, Suita, 564-8680, Japan
b) Department of Mathematical Sciences, Kwansei Gakuin University, Sanda, 669-1337, Japan

Received October 11, 2013, in final form April 16, 2014; Published online April 22, 2014

Abstract
Higher KdV flows on spaces of closed equicentroaffine plane curves are studied and it is shown that the flows are described as certain multi-Hamiltonian systems on the spaces. Multi-Hamiltonian systems describing higher mKdV flows are also given on spaces of closed Euclidean plane curves via the geometric Miura transformation.

Key words: motions of curves; equicentroaffine curves; KdV hierarchy; multi-Hamiltonian systems.

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