Surfaces associated with theta function solutions of the periodic 2D-Toda lattice
نویسندگان
چکیده
The objective of this paper is to present some geometric aspects of surfaces associated with theta function solutions of the periodic 2D-Toda lattice. For this purpose we identify the (N − 1)-dimensional Euclidean space with the su(N) algebra which allows us to construct the generalized Weierstrass formula for immersion for such surfaces. The elements characterizing surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations, the Gaussian curvature, the mean curvature vector and theWilmore functional of a surface are expressed explicitly in terms of any theta function solution of the Toda lattice model. We have shown that these surfaces are all mapped into subsets of a hypersphere in
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