The purpose of this article is to
characterize Minkowski general G-spaces. The unit sphere K is shown to have at
most four components.
Assume the space R is not reducible. If K has one component, R is an ordinary
Minkowski G-space. If K has two components they are quadrics and R is nearly
pseudoeuclidean. When K has three components, one is a quadric and the other two
are strictly convex. The unit sphere has four components only in dimension
two.