  In earlier papers we changed the concept of the inner product to a more
general one, to the so-called Minkowski product. This product changes on the
tangent space hence we could investigate a more general structure than a
Riemannian manifold. Particularly interesting such a model when the negative
direct component has dimension one and the model shows certain space-time
character. We will discuss this case here. We give a deterministic and a
non-deterministic (random) variant of a such a model. As we showed, the
deterministic model can be defined also with a "shape function".
