  We study new examples of translating solitons of the mean curvature flow,
especially in Minkowski space. We consider for this purpose manifolds admitting
submersions and cohomegeneity one actions by isometries on suitable open
subsets. This general setting also covers the classical Euclidean examples. As
an application, we completely classify timelike, invariant translating solitons
by rotations and boosts in Minkowski space.
