  A class of curved spacetimes with global parabolic isometries (GPI) is
introduced. These isometries have fixed point sets on two-dimensional null
surfaces which can be interpreted as worldsheets of massless cosmic strings.
Back reaction effects of the strings in such spacetimes can be described
exactly, in terms of a nontrivial holonomy at the worldsheet. We show that the
GPI spacetimes are type $N$ geometries of the Petrov classification. We
describe a number of features of these spacetimes, including properties of
Killing horizons associated to GPI. As an example, we consider a circular
massless cosmic string in the de Sitter universe and present the metric in new
coordinates centered at the string worldsheet.
