Published online by Cambridge University Press: 24 October 2008
A generalization of the notion of Riemannian submersion is given for submersions of a Lorentzian manifold onto a Riemannian manifold of one lower dimension. These maps are called comersions. A comersion induces a surjection of the space of causal curves in the domain manifold onto curves of bounded length in the image manifold. Thus if the source space is causally 1-connected, the target space is 1-connected.