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<p>In this paper, we study a class of Finsler metrics of cohomogeneity not exceeding 2 on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_671_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}} \times {\mathbb {R}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">R</mi> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>. These metrics not only contain Finsler warped product metrics introduced by Marçal and Shen, but also contain the normalized Einstein universe in general relativity. We obtain the PDE characterization for these metrics to be Einstein refining the result of Marçal and Shen. Infinitely many <i>new</i> non-Riemannian Ricci-flat Finsler metrics of this type are constructed.</p>

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On a class of Einstein–Finsler metrics with cohomogeneity not exceeding 2

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • H. Liu,
  • X. Mo,
  • H. Zhang

摘要

In this paper, we study a class of Finsler metrics of cohomogeneity not exceeding 2 on \({\mathbb {R}} \times {\mathbb {R}}^n\) R × R n . These metrics not only contain Finsler warped product metrics introduced by Marçal and Shen, but also contain the normalized Einstein universe in general relativity. We obtain the PDE characterization for these metrics to be Einstein refining the result of Marçal and Shen. Infinitely many new non-Riemannian Ricci-flat Finsler metrics of this type are constructed.