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Lorentzian Algebraic Ricci Solitons on the Heisenberg Group
Abstract
There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group H2n+1, or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra h2n+1, denoted by μ, ν, and ϕ. We show that, in a specific case, μ is an algebraic Ricci soliton that is shrinking. Moreover, ν is an algebraic Ricci soliton only on the three-dimensional Heisenberg Lie algebra h3 and it is shrinking. Finally, we show that ϕ is a steady algebraic Ricci soliton on h2n + 1 for n > 1. However, for n = 1, ϕ is flat.
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BibTeX
@misc{ayad2026lorentzian,
title = {{Lorentzian Algebraic Ricci Solitons on the Heisenberg Group}},
author = {Youssef Ayad},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17183},
eprint = {2609.17183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17183},
}
RIS
TY - UNPB
TI - Lorentzian Algebraic Ricci Solitons on the Heisenberg Group
AU - Youssef Ayad
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17183
UR - https://arxiv.org/abs/2609.17183
AB - There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group H_2n+1, or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra h_2n+1, denoted by μ, ν, and ϕ. We show that, in a specific case, μ is an algebraic Ricci soliton that is shrinking. Moreover, ν is an algebraic Ricci soliton only on the three-dimensional Heisenberg Lie algebra h_3 and it is shrinking. Finally, we show that ϕ is a steady algebraic Ricci soliton on h_2n + 1 for n > 1. However, for n = 1, ϕ is flat.
ER -