Mathematics > Differential Geometry
[Submitted on 1 Jun 2009 (v1), last revised 3 Jul 2009 (this version, v2)]
Title:Lorentz Ricci solitons on 3-dimensional Lie groups
View PDFAbstract: The three-dimensional Heisenberg group H_3 has three left-invariant Lorentz metrics g_1, g_2 and g_3. They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric g_1 as a Lorentz Ricci soliton. This Ricci soliton g_1 is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) and the isometry group of flat Lorentz plane E(1,1) have Lorentz Ricci solitons.
Submission history
From: Kensuke Onda [view email][v1] Mon, 1 Jun 2009 13:02:53 UTC (5 KB)
[v2] Fri, 3 Jul 2009 10:10:36 UTC (7 KB)
Current browse context:
math.DG
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.