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We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions and , based on the algebraic approach of such spaces through the notion of a pseudo-Riemannian weakly symmetric Lie algebra. We also study the general symmetry of reductive -dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a -dimensional reductive -fold symmetric pseudo-Riemannian manifold must be globally symmetric.
A trans-Sasakian 3-manifold is pseudo-symmetric if and only if it is η-Einstein. In particular, a quasi-Sasakian 3-manifold is pseudo-symmetric if and only if it is a coKähler manifold or a homothetic Sasakian manifold. Some examples of non-Sasakian pseudo-symmetric contact 3-manifolds are exhibited.
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 .
The present paper is concerned with obtaining a classification regarding to four-dimensional semi-symmetric neutral Lie groups. Moreover, we discuss some geometric properties of these spaces. We exhibit a rich class of non-Einstein Ricci soliton examples.
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