Reduction in the model of a relativistic string for arbitrary dimension of Minkowski space

It is shown that the equations describing the dynamics of a classical relativistic string in $d$-dimensional space-time reduce to a system of $d-2$ nonlinear partial differential equations. These equations determine an embedding of a two-dimensional minimal surface in $d$-dimensional pseudo-Euclidean space. Two gauges used in string theory are considered: the timelike gauge and the relativistically invariant gauge.