On integrable systems in 3-dimensional Riemannian geometry

Beffa, Gloria Marì and Sanders, Jan A. and Wang, Jing Ping (2002) On integrable systems in 3-dimensional Riemannian geometry. Journal of Nonlinear Science, 12 (2). pp. 143-167. ISSN 0938-8974. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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.

Item Type: Article
Uncontrolled keywords: Riemannian Geometry, geometric evolutions, integrable systems, Poisson structures
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Jing Ping Wang
Date Deposited: 09 Oct 2008 18:05
Last Modified: 17 Jun 2014 11:16
Resource URI: https://kar.kent.ac.uk/id/eprint/8819 (The current URI for this page, for reference purposes)
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