Exact solutions for a zero-string in Lorentzian spacetimes with a nontrivial conformal group

We study the dynamics of a zero-string for a broad class of Lorentzian spacetimes with a nontrivial conformal group. Exact solutions for a closed zero-string is found for all spacetimes from this class in a general view. It is shown that such a set of primary data exists in these spacetimes, for which the closed zero-string does not interact with the outward background field. The obtained results can be served as a basis for investigation of zero-strings in the fields of shock electromagnetic and gravitational waves. They also can be used as a zero approach to research the dynamics of strings within the theory of perturbations, where the role of small parameter is played by the tension of a string