  The tangent hyperplanes of the "manifolds" of this paper equipped a so-called
Minkowski product. It is neither symmetric nor bilinear. We give a method to
handing such an object as a locally hypersurface of a generalized space-time
model and define the main tools of its differential geometry: its fundamental
forms, its curvatures and so on. In the case, when the fixed space-time
component of the embedding structure is a continuously differentiable
semi-inner product space, we get a natural generalization of some important
semi-Riemann manifolds as the hyperbolic space, the de Sitter sphere and the
light cone of a Minkowski-Lorenz space, respectively.
