(H, C)-groups with positive line bundles

Abstract

Let G be a connected complex Lie group. Then there exists the smallest closed complex subgroup G0 of G such that G/G0 is a Stein group (Morimoto). Moreover G0 is a connected abelian Lie group and every holomorphic function on G0 is a constant. G0 is called an (H, C)-group or a toroidal group. Every connected complex abelian Lie group is isomorphic to the direct product G0 × Cm × C*n, where G0 is an (H,C)-group.