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Pseudo-Riemannian weakly symmetric manifolds of low dimension

Bo Zhang, Zhiqi Chen, Shaoqiang Deng (2019)

Czechoslovak Mathematical Journal

We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions 2 and 3 , 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 3 -dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a 3 -dimensional reductive 2 -fold symmetric pseudo-Riemannian manifold must be globally symmetric.

Pseudo-symmetric contact 3-manifolds III

Jong Taek Cho, Jun-ichi Inoguchi, Ji-Eun Lee (2009)

Colloquium Mathematicae

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.

Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

H. Shiga, M. Tezuka (1987)

Annales de l'institut Fourier

We show that an orientable fibration whose fiber has a homotopy type of homogeneous space G / U with rank G = rang U is totally non homologous to zero for rational coefficients. The Jacobian formed by invariant polynomial under the Weyl group of G plays a key role in the proof. We also show that it is valid for mod. p coefficients if p does not divide the order of the Weyl group of G .

Reductive homogeneous spaces and nonassociative algebras

Alberto Elduque (2020)

Communications in Mathematics

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.

Riemannian symmetries in flag manifolds

Paola Piu, Elisabeth Remm (2012)

Archivum Mathematicum

Flag manifolds are in general not symmetric spaces. But they are provided with a structure of ℤ 2 k -symmetric space. We describe the Riemannian metrics adapted to this structure and some properties of reducibility. The conditions for a metric adapted to the ℤ 2 2 -symmetric structure to be naturally reductive are detailed for the flag manifold S O ( 5 ) / S O ( 2 ) × S O ( 2 ) × S O ( 1 ) .

Semi-symmetric four dimensional neutral Lie groups

Ali Haji-Badali, Amirhesam Zaeim (2020)

Czechoslovak Mathematical Journal

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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