ON ODD-DIMENSIONAL COMPLEX ANALYTIC KLEINIAN GROUPS

We shall explain here an idea to generalize classical complex analytic Kleinian group theory to any odd-dimensional cases. For a certain class of discrete subgroups of PGL2n +1(C) acting on P2n+1, we can define their domains of discontinuity in a canonical manner, regarding an n-dimensional projective linear subspace in P2n+1 as a point, like a point in the classical one-dimensional case. Many interesting (compact) non-K <spacing diaeresis>ahler manifolds appear systematically as the canonical quotients of the domains. In the last section, we shall give some examples.