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
atefeh.toohidfar@gmail.com
Amirhesam Zaeim
Department of Mathematics, Payame Noor University, Tehran, Iran
zaeim@pnu.ac.ir
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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