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<p>In this paper, using the new curvature conditions for Bochner techniques recently provided by Petersen and Wink, we introduce some novel vanishing results for weighted <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13163_2025_552_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^Q\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>Q</mi> </msup> </math></EquationSource> </InlineEquation> harmonic <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13163_2025_552_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation>-forms on smooth metric measure spaces. We emphasize that the domain of <i>Q</i> in our investigation is <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13163_2025_552_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q&gt;\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>Q</mi> <mo>&gt;</mo> </mrow> </math></EquationSource> </InlineEquation> 1, which represents an improvement over previous works. Finally, we derive a vanishing theorem for (0,&#xa0;2) weighted harmonic symmetric traceless tensors.</p>

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On vanishing results for smooth metric measure spaces with weighted curvature tensors

  • 期刊论文

  • 发表日期：

    2025年10月26日

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  • Ha Tuan Dung,
  • Nguyen Thac Dung,
  • Thieu Dinh Minh Hung

摘要

In this paper, using the new curvature conditions for Bochner techniques recently provided by Petersen and Wink, we introduce some novel vanishing results for weighted \(L^Q\) L Q harmonic \(\ell \) ℓ -forms on smooth metric measure spaces. We emphasize that the domain of Q in our investigation is \(Q>\) Q > 1, which represents an improvement over previous works. Finally, we derive a vanishing theorem for (0, 2) weighted harmonic symmetric traceless tensors.