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Journal of Lie Theory 31 (2021), No. 1, 169--187
Copyright Heldermann Verlag 2021

On Pseudo-Riemannian Cyclic Homogeneous Manifolds of Dimension Four

Atefeh Tohidfar
Institute of Advanced Studies, Payame Noor University, Tehran, Iran

Amirhesam Zaeim
Department of Mathematics, Payame Noor University, Tehran, Iran

We study the homogeneous structures of pseudo-Riemannian Lie groups of signature (2,2). This study allows us to classify the cyclic Lie groups of the mentioned signature. We also study the cyclic pseudo-Riemannian homogeneous 4-manifolds with non-trivial isotropy.

Keywords: Pseudo-Riemannian Lie groups, left-invariant cyclic metrics, homogeneous pseudo-Riemannian structures, non-trivial isotropy.

MSC: 53B30, 53C30, 22E25, 22E46.

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