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In this work we establish a form of the fundamental theorem regarding immersions of lightlike hypersurfaces in the Cartesian product \( \mathbb {R}\times \mathbb {Q}^{n+1}_{c,1}\) , where \(\mathbb {Q}^{n+1}_{c,1}\) denotes a Lorentzian space form of constant sectional curvature c. Namely, we establish necessary and sufficient conditions for the existence of an isometric immersion \(\phi \) of a smooth \((n+1)\) -dimensional manifold M endowed with a degenerate metric g on \( \mathbb {R}\times \mathbb {Q}^{n+1}_{c,1}\) , provided that \(\partial _t\in \varGamma (\phi (M))\) .

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Isometric Lightlike Immersions in \( \mathbb {R}\times \mathbb {Q}^{n+1}_{c,1}\)

  • 会议论文

  • 发表日期：

    2025年

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

摘要

In this work we establish a form of the fundamental theorem regarding immersions of lightlike hypersurfaces in the Cartesian product \( \mathbb {R}\times \mathbb {Q}^{n+1}_{c,1}\) , where \(\mathbb {Q}^{n+1}_{c,1}\) denotes a Lorentzian space form of constant sectional curvature c. Namely, we establish necessary and sufficient conditions for the existence of an isometric immersion \(\phi \) of a smooth \((n+1)\) -dimensional manifold M endowed with a degenerate metric g on \( \mathbb {R}\times \mathbb {Q}^{n+1}_{c,1}\) , provided that \(\partial _t\in \varGamma (\phi (M))\) .