Prehomogeneous vector spaces and ergodic theory II

We apply M. Ratner's theorem on closures of unipotent orbits to the study o f three families of prehomogeneous vector spaces. As a result, we prove ana logues of the Oppenheim Conjecture for simultaneous approximation by values of certain alternating bilinear forms in an even number of variables and c ertain alternating trilinear forms in six and seven variables.