A Characterization of Complex Homogeneous Cones.
We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.
Let be a connected complex Lie group, a closed, complex subgroup of and . Let be the radical and a maximal semisimple subgroup of . Attempts to construct examples of noncompact manifolds homogeneous under a nontrivial semidirect product with a not necessarily -invariant Kähler metric motivated this paper. The -orbit in is Kähler. Thus is an algebraic subgroup of [4]. The Kähler assumption on ought to imply the -action on the base of any homogeneous fibration is algebraic...
Dans cet article, j’étudie le groupe des automorphismes analytiques d’un domaine de Reinhardt borné d’un espace de Banach complexe à base. Je montre que, dans certains cas, ce groupe est un groupe de Lie banachique réel et je donne une classification complète des domaines de Reinhardt bornés homogènes. Pour certains espaces de Banach, je montre que les seuls automorphismes analytiques de la boule-unité ouverte sont linéaires.