  A systematic group theoretical formulation of the Pohlmeyer reduction is
presented. It provides a map between the equations of motion of sigma models
with target-space a symmetric space M=F/G and a class of integrable
multi-component generalizations of the sine-Gordon equation. When M is of
definite signature their solutions describe classical bosonic string
configurations on the curved space-time R_t\times M. In contrast, if M is of
indefinite signature the solutions to those equations can describe bosonic
string configurations on R_t\times M, M\times S^1_\vartheta or simply M. The
conditions required to enable the Lagrangian formulation of the resulting
equations in terms of gauged WZW actions with a potential term are clarified,
and it is shown that the corresponding Lagrangian action is not unique in
general. The Pohlmeyer reductions of sigma models on CP^n and AdS_n are
discussed as particular examples of symmetric spaces of definite and indefinite
signature, respectively.
