Levi-curvature of manifolds with a Stein rational fibration (Q1065971)

Let G/H be a homogeneous manifold in which a maximal compact subgroup K of G has real hypersurface orbits. Then it is known that, under some restrictions, G/H fibres over a homogeneous rational manifold G/P with Stein fibre P/H. In this paper a natural exhaustion function for G/H is constructed and the eigenvalues of its Levi form are computed. The proofs relies deeply on the geometry of linear algebraic groups.