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<p>In this paper, we show that there do not exist Hopf hypersurfaces with semi-parallel Ricci tensor in both of two Hermitian symmetric spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_753_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q^m\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>Q</mi> <mi>m</mi> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_753_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q^{m*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>Q</mi> <mrow /> <mrow> <mi>m</mi> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="22_2025_753_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>m</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation></p>

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Non-existence of Hopf hypersurfaces with semi-parallel Ricci tensor in both the complex quadric and the complex hyperbolic quadric

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Dehe Li,
  • Xi Zhang

摘要

In this paper, we show that there do not exist Hopf hypersurfaces with semi-parallel Ricci tensor in both of two Hermitian symmetric spaces \(Q^m\) Q m and \(Q^{m*}\) Q m ∗ for \(m\ge 3\) m ≥ 3