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Abstract <p> We regard a Box-quasimetric on a canonical Engel group as a symmetric<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5123_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\((q_1,q_2)\)</EquationSource> </InlineEquation>-quasimetric and find a description of the domain ofadmissible parameters <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5123_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_1\)</EquationSource> </InlineEquation> and<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5123_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(q_2\)</EquationSource> </InlineEquation> and an implicit form of the least constant<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5123_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\)</EquationSource> </InlineEquation> in the <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12002_2025_5123_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\((q,q)\)</EquationSource> </InlineEquation>-generalized triangle inequality.</p>

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The Domain of Admissible Parameters of a Box-Quasimetric on a Canonical Engel Group

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. V. Greshnov,
  • S. A. Greshnova

摘要

Abstract

We regard a Box-quasimetric on a canonical Engel group as a symmetric \((q_1,q_2)\) -quasimetric and find a description of the domain ofadmissible parameters \(q_1\) and \(q_2\) and an implicit form of the least constant \(q\) in the \((q,q)\) -generalized triangle inequality.