We show that an orientable fibration whose fiber has a homotopy type of homogeneous space with rank is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of plays a key role in the proof. We also show that it is valid for mod. coefficients if does not divide the order of the Weyl group of .
In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.
The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu [Nom54] that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.
If N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then [...] for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a viewpoint of Lie algberas.
Flag manifolds are in general not symmetric spaces. But they are provided with a structure of -symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the -symmetric structure to be naturally reductive are detailed for the flag manifold .