Journal
ANALYSIS AND MATHEMATICAL PHYSICS
Volume 12, Issue 2, Pages -Publisher
SPRINGER BASEL AG
DOI: 10.1007/s13324-022-00669-7
Keywords
Ricci soliton; Left-invariant Lorentz metric; pp-wave
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Funding
- AEI/FEDER, Spain [PID2019-105138GB-C21]
- Xunta de Galicia, Spain [ED431C 2019/10, ED431F 2020/04]
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This article investigates non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups with left-invariant soliton vector fields. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian metrics on semi-direct extensions R-3 (sic) R and E(1, 1) (sic) R. It is shown that some of these Ricci solitons are conformally Einstein and can be expanding, steady, or shrinking.
We determine all non-Einstein Ricci solitons on four-dimensional Lorentzian Lie groups whose soliton vector field is left-invariant. In addition to pp-wave and plane wave Lie groups, there are four families of Lorentzian metrics on semi-direct extensions R-3 (sic) R and E(1, 1) (sic) R. We show that some of these Ricci solitons are conformally Einstein and they may be expanding, steady or shrinking.
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