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A generalized formula for integrable classes of surfaces in Lie algebras (1997)

Cies´linski, Jan

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 38 (1997), S. 4255-4272

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: We discuss relations between the approach of Fokas and Gelfand to immersions on Lie algebras and the theory of soliton surfaces of Sym. We show that many results concerning immersions on Lie algebras can be reduced to or interpreted within the soliton surfaces approach. We present also some new results, including a generalization of the Fokas–Gelfand formula for integrable classes of surfaces in Lie algebras [and, in particular, in (pseudo)-Euclidean n-dim. spaces]. The generalized formula is used to formulate a method of constructing integrable classes of surfaces. As an example we discuss the class of linear Weingarten surfaces defined by the linear relationship between Gaussian and mean curvatures. We construct explicitly a one-parameter family of linear Weingarten surfaces parallel (equidistant) to a given pseudospherical surface. © 1997 American Institute of Physics.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.532093

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