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<p>In Cho et al. (Results Math 77(3):16, 2022), the authors defined the notion of the weakly <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2966_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Einstein structure on almost contact metric manifolds. In this paper, we investigate some classes of three-dimensional almost contact metric manifolds with weakly <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2966_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Einstein structures. In particular, we classify the contact metric manifold, the almost cosymplectic manifold and the almost Kenmotsu manifold.</p>

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A Classification of Three-Dimensional Weakly \(\eta \)-Einstein Manifolds

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Sun Hyang Chun,
  • Yunhee Euh

摘要

In Cho et al. (Results Math 77(3):16, 2022), the authors defined the notion of the weakly \(\eta \) η -Einstein structure on almost contact metric manifolds. In this paper, we investigate some classes of three-dimensional almost contact metric manifolds with weakly \(\eta \) η -Einstein structures. In particular, we classify the contact metric manifold, the almost cosymplectic manifold and the almost Kenmotsu manifold.