Generalization of the relativistic string model in the geometrical approach

Abstract

We present a model of a one-dimensional extended relativistic object, whose motion is defined by the requirement that its time track in Minkowski space is a surface of the constant mean curvature H. The world surface of the relativistic string is a particular case of such surfaces, namely, a minimal surface with H=0. By differential-geometry methods the theory of the proposed object moving in three-dimensional space-time is reduced to one nonlinear equation ϕ_ττ − ϕ_σσ = Hshϕ. In the theory under consideration, there naturally arises the pair of Lax's operators needed to solve this nonlinear equation by the inverse scattering method.