Surfaces associated with theta function solutions of the periodic 2D-Toda lattice

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dc.creatorGrundland, A. M.
dc.creatorMo, M. Y.
dc.date2006-05-03
dc.date.accessioned2026-07-07T07:13:52Z
dc.date.available2026-07-07T07:13:52Z
dc.descriptionThe 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 $(N^2-1)$-dimensional Euclidean space with the ${\frak su}(N)$ 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 the Wilmore 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 $\mathbb{R}^{N^2-1}$. A detailed implementations of the obtained results are presented for surfaces immersed in the ${\frak su}(2)$ algebra and we show that different Toda lattice data correspond to different subsets of a sphere in $\mathbb{R}^3$.
dc.description35 pages
dc.identifierhttps://arxiv.org/abs/math/0605081
dc.identifierhttp://arxiv.org/abs/math/0605081
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112639
dc.subjectDifferential Geometry
dc.subject14J81
dc.titleSurfaces associated with theta function solutions of the periodic 2D-Toda lattice
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