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<p>We apply some maximum principles to establish rigidity results concerning complete spacelike weighted translating solitons immersed in a weighted Lorentzian product space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13366_2025_789_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}_1\times {\mathbb {P}}^n_f\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">R</mi> <mn>1</mn> </msub> <mo>×</mo> <msubsup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>f</mi> <mi>n</mi> </msubsup> </mrow> </math></EquationSource> </InlineEquation> endowed with a potential function <i>f</i> and whose Riemannian base <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13366_2025_789_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {P}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> is supposed to be complete and with nonnegative Bakry–Émery–Ricci tensor. As applications, we derive new Calabi–Bernstein type results for entire spacelike weighted translating graphs constructed over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13366_2025_789_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {P}}^n.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>n</mi> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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A note on spacelike weighted translating solitons in weighted Lorentzian product spaces

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Henrique Fernandes de Lima

摘要

We apply some maximum principles to establish rigidity results concerning complete spacelike weighted translating solitons immersed in a weighted Lorentzian product space \({\mathbb {R}}_1\times {\mathbb {P}}^n_f\) R 1 × P f n endowed with a potential function f and whose Riemannian base \({\mathbb {P}}^n\) P n is supposed to be complete and with nonnegative Bakry–Émery–Ricci tensor. As applications, we derive new Calabi–Bernstein type results for entire spacelike weighted translating graphs constructed over \({\mathbb {P}}^n.\) P n .