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Abstract <p>The authors investigate a model of the Defrise Universe DU as a Lie group <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8216_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_{4}\)</EquationSource> <!--LobJMat2560512Berestovskii-m1--> </InlineEquation> with a left-invariant Lorentz metric and find by two methods its geodesics (they are not closed and may be incomplete), all Killing vector fields, structures of the Lie algebra of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8216_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_{4},\)</EquationSource> <!--LobJMat2560512Berestovskii-m2--> </InlineEquation> the isometry Lie group <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8216_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_{6}\)</EquationSource> <!--LobJMat2560512Berestovskii-m3--> </InlineEquation> of the Defrise Universe DU and its subgroups. We also describe all possible types of induced sub-Lorentz structures on DU up to isomorphisms of the Lie group <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8216_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_{4}\)</EquationSource> <!--LobJMat2560512Berestovskii-m4--> </InlineEquation>.</p>

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Geodesics and Isometry Group of Defrise Universe as a Lie Group with Left-invariant Lorentz Metric

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • V. N. Berestovskii,
  • I. A. Zubareva

摘要

Abstract

The authors investigate a model of the Defrise Universe DU as a Lie group \(G_{4}\) with a left-invariant Lorentz metric and find by two methods its geodesics (they are not closed and may be incomplete), all Killing vector fields, structures of the Lie algebra of \(G_{4},\) the isometry Lie group \(G_{6}\) of the Defrise Universe DU and its subgroups. We also describe all possible types of induced sub-Lorentz structures on DU up to isomorphisms of the Lie group \(G_{4}\) .