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<p>In this work, we determine necessary and sufficient conditions for the existence of an isometric immersion of a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2988_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\((n+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-manifold with a degenerate metric in product manifolds of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2988_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation> with Lorentzian space forms and also in product manifolds of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2988_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(-{\mathbb {R}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>-</mo> <mi mathvariant="double-struck">R</mi> </mrow> </math></EquationSource> </InlineEquation> with Riemannian space forms.</p>

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Isometric Immersions of Lightlike Manifolds in Lorentzian Products

  • 期刊论文

  • 发表日期：

    2025年11月3日

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  • Carlos Avila,
  • Matias Navarro,
  • Oscar Palmas,
  • Didier A. Solis

摘要

In this work, we determine necessary and sufficient conditions for the existence of an isometric immersion of a \((n+1)\) ( n + 1 ) -manifold with a degenerate metric in product manifolds of \({\mathbb {R}}\) R with Lorentzian space forms and also in product manifolds of \(-{\mathbb {R}}\) - R with Riemannian space forms.