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<p>In this paper, we have proved a weighted Laplacian comparison of distance function for manifolds with Bakry–Émery curvature bounded from below. Next, we have shown that a gradient <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1284_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation>-Einstein soliton with a bounded integral condition on Ricci curvature splits off a line isometrically. Moreover, using this result, we have established some boundedness conditions on scalar curvature of gradient <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1284_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ρ</mi> </math></EquationSource> </InlineEquation>-Einstein soliton.</p>

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Splitting theorem of gradient \(\rho \)-Einstein solitons

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Absos Ali Shaikh,
  • Prosenjit Mandal,
  • Chandan Kumar Mondal

摘要

In this paper, we have proved a weighted Laplacian comparison of distance function for manifolds with Bakry–Émery curvature bounded from below. Next, we have shown that a gradient \(\rho \) ρ -Einstein soliton with a bounded integral condition on Ricci curvature splits off a line isometrically. Moreover, using this result, we have established some boundedness conditions on scalar curvature of gradient \(\rho \) ρ -Einstein soliton.