In the framework of the study of homogeneous Lorentzian three-manifolds, we consider here the only class of examples which admit a four-dimensional group of isometries but are neither Lorentzian Bianchi–Cartan–Vranceanu spaces nor plane waves. We obtain an explicit description in global coordinates of these special homogeneous Lorentzian manifolds. We then prove that all such examples are non-gradient expanding Ricci solitons.
Accepted:
Keywords: Lorentzian Lie groups, isometry groups, Ricci solitons
Calvaruso, Giovanni 1 ; Pellegrino, Lorenzo 1 ; Zaeim, Amirhesam 2
Calvaruso, Giovanni; Pellegrino, Lorenzo; Zaeim, Amirhesam. Ricci solitons of special Lorentzian Lie groups with a four-dimensional isometry group. Journal of Lie Theory, Online first, pp. 1-11
@unpublished{10_5802_jolt_1430,
author = {Calvaruso, Giovanni and Pellegrino, Lorenzo and Zaeim, Amirhesam},
title = {Ricci solitons of special {Lorentzian} {Lie} groups with a four-dimensional isometry group},
journal = {Journal of Lie Theory},
publisher = {XXXX},
doi = {10.5802/jolt.1430},
language = {en},
note = {Online first},
}
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