On the geometry of Lorentz orbit spaces

The orbit space of the Lorentz group acting on the product ofn real, or complex, Minkowski spaces is stratified into subspaces isomorphic to certain products of Grassmann manifolds and varieties of Gram matrices. The Lorentz orbits (of nonzero dimension) are completely classified by the Stiefel manifolds of standard orthogonal bases for the linear subspaces of the Minkowski space. Several representations of the spaces ofn-point Lorentz invariant distributions and differentiable, or analytic, functions onto appropriate spaces of distributions and functions of Lorentz invariant variables are also discussed.On leave of absence from the Institute of Atomic Physics, Bucharest, Romania.