A class of nonlinear sigma-models coupled to gravity is defined by identifying the coordinates of spacetime with the components of a set of scalar fields. The obtained theories have purely geometric character, and necessarily possess soliton solutions with topologically non-trivial scalar sectors. In some cases, the corresponding configuration spaces are shown to possess the necessary homotopy structure to admit fermions. The stability problem is considered only in the asymptotic region of the soliton solutions. It is shown how the asymptotic flatness of the soliton metric leads to the compactification of the sigma-model target space. As an illustration, the examples of a cosmic string solution and a monopole solution are considered.