Integrable systems in three-dimensional Riemannian geometry

G. Marí Beffa, J.A. Sanders, J.P. Wang

Research output: Contribution to JournalArticleAcademicpeer-review


In this paper we introduce a new infinite-dimensional pencil of Hamiltonian structures. These Poisson tensors appear naturally as the ones governing the evolution of the curvatures of certain flows of curves in 3-dimensional Riemannian manifolds with constant curvature. The curves themselves are evolving following arclength-preserving geometric evolutions for which the variation of the curve is an invariant combination of the tangent, normal, and binormal vectors. Under very natural conditions, the evolution of the curvatures will be Hamiltonian and, in some instances, bi-Hamiltonian and completely integrable.
Original languageEnglish
Pages (from-to)143-167
JournalJournal of nonlinear science
Issue number2
Publication statusPublished - 2002

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