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18
Surfaces in terms of 2 by 2 matrices. Old and new integrable cases
, 1994
"... this paper 118 A.I. Bobenko where is of the form (8.21). Then the immersion function F = 2\Psi ..."
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Cited by 67 (6 self)
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this paper 118 A.I. Bobenko where is of the form (8.21). Then the immersion function F = 2\Psi
The principal chiral model as an integrable system
 in Harmonic Maps and Integrable Systems, Aspects Math
, 1994
"... ..."
Infinite dimensional Lie groups and the twodimensional Toda lattice, in Harmonic maps and integrable systems, ed: A
 P Fordy & J C Wood, Aspects of Mathematics E23, Vieweg
, 1994
"... ..."
Integrable Systems, Harmonic Maps and the Classical Theory of Surfaces
 Aspects Math
, 1994
"... this paper. ..."
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The affine Toda equations and minimal surfaces
 In Harmonic Maps and Integrable Systems
, 1993
"... this article we consider geometrical interpretations of the twodimensional affine Toda equations for a compact simple Lie group G. These equations originated from the work of Toda [33],[34] over 25 years ago on vibrations of lattices, and they have received considerable attention from both pure and ..."
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this article we consider geometrical interpretations of the twodimensional affine Toda equations for a compact simple Lie group G. These equations originated from the work of Toda [33],[34] over 25 years ago on vibrations of lattices, and they have received considerable attention from both pure and applied mathematicians particularly over the last 15 years. (For the original context of the ideas the reader is referred to [35], [27] and [1] and for a survey of recent work to [29] and [21]).
Twistors, Nilpotent Orbits and Harmonic Maps
"... this paper we shall be interested in compact homogeneous quaternionKahler manifolds. They were classified by Wolf and Alekseevskii ([39, 1]). They are symmetric and are known as Wolf spaces. There is one such manifold for each compact simple Lie algebra g and it can be defined in the following way. ..."
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Cited by 4 (0 self)
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this paper we shall be interested in compact homogeneous quaternionKahler manifolds. They were classified by Wolf and Alekseevskii ([39, 1]). They are symmetric and are known as Wolf spaces. There is one such manifold for each compact simple Lie algebra g and it can be defined in the following way. Let t be a maximal torus in g. Take the su(2) in g with the root system fae; \Gammaaeg where ae is the highest root. The conjugacy class M = G=NG (su(2)) of such su(2) is the Wolf space corresponding to the Lie algebra g (G denotes a compact simple Lie group with Lie algebra g and NG (su(2)) is the normaliser of su(2) in G). One can write M as G=
2dimensional nonlinear sigma models: zero curvature and Poisson structure
"... In this chapter some aspects of twodimensional nonlinear sigma models are discussed. The solutions to the field equations are (pseudo)harmonic maps of twodimensional Minkowski space into some homogeneous Riemannian manifolds. In Section 2 we shall give a brief introduction to the physics of these ..."
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In this chapter some aspects of twodimensional nonlinear sigma models are discussed. The solutions to the field equations are (pseudo)harmonic maps of twodimensional Minkowski space into some homogeneous Riemannian manifolds. In Section 2 we shall give a brief introduction to the physics of these models and discuss the conditions under which a zero curvature ansatz built out of the conserved currents is possible: Theorem (2.1) which is an extended version of old work of the physicists K. Pohlmeyer [29] and H. Eichenherr & M. Forger [11] shows under weak technical assumptions that such an ansatz works if and only if the target manifold is a (pseudo)Riemannian symmetric space. We have included the rather technical, mainly Lie algebraic proof because the result is new (although not very surprising). The use of symmetric spaces in this context had recently been rediscovered in the mathematics literature (see, for example [31]) and applied to harmonic tori, see for...
BIHARMONIC MAPS INTO COMPACT LIE GROUPS AND THE INTEGRABLE SYSTEMS
, 910
"... Abstract. In this paper, the reduction of biharmonic map equation in terms of the MaurerCartan form for all smooth map of an arbitrary compact Riemannian manifold into a compact Lie group (G, h) with biinvariant Riemannian metric h is obtained. By this formula, all biharmonic curves into compaqct ..."
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Abstract. In this paper, the reduction of biharmonic map equation in terms of the MaurerCartan form for all smooth map of an arbitrary compact Riemannian manifold into a compact Lie group (G, h) with biinvariant Riemannian metric h is obtained. By this formula, all biharmonic curves into compaqct Lie groups are determined, and all the biharmonic maps of an open domain of R 2 with the conformal metric of the standard Riemannian metric into (G, h) are determined.