. D G ] 2 3 Ju l 1 99 8 Weierstrass representations for surfaces in 4 D spaces and their integrable deformations via DS hierarchy
نویسنده
چکیده
Generalized Weierstrass representations for generic surfaces confor-mally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willmore functional of a surface is invariant under such deformations.
منابع مشابه
Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and
Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy. Abstract Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfa...
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Generalizations of the Weierstrass formulae to generic surface immersed into R 4 , S 4 and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
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It is shown that the equation which describes constant mean curvature surfaces via the generalized Weierstrass–Enneper inducing has Ha-miltonian form. Its simplest finite–dimensional reduction is the integrable Hamiltonian system with two degrees of freedom. This finite-dimensional system admits S 1-action and classes of S 1-equivalence of its trajectories are in one-to-one correspondence with ...
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