Sanders, J.A. and Wang, J.P. (2006) Integrable systems in n-dimensional conformal geometry. Journal of Difference Equations and Applications, 12 (10). pp. 983-995. ISSN 1563-5120 (electronic) 1023-6198 (paper) .
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In this paper we show that if we write down the structure equations for the flow of the parallel frame of a curve embedded in a flat n-dimensional conformal manifold, this leads to two compatible Hamiltonian operators. The corresponding integrable scalar-vector equation is where is the standard Euclidean inner product of the vector with itself. These results are similar to those we obtained in the Riemannian case, implying that the method employed is well suited for the analysis of the connection between geometry and integrability.
|Uncontrolled keywords:||Standard Euclidean; Riemannian case; Hamiltonian operator; Hasimoto transformation|
|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:||23 Sep 2008 12:39|
|Last Modified:||14 Jan 2010 14:32|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/8794 (The current URI for this page, for reference purposes)|
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