Smooth kinematic-type manifolds

We propose a general approach for describing different causality-type relations on smooth manifolds. The causality structure can be defined either axiomatically (by a cone in the tangent space) or by a pseudometric with the signature $(+-\cdots-)$ or $(+-\cdots-0\cdots0)$. In the latter case, the manifold acquires the structure of a fibered space with “absolute simultaneity” fibers. The smooth structure (atlas) of the manifold is directly related to its causal structure.