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<p>In this paper we investigate hypersurfaces in non-flat Lorentzian space forms that carry a totally geodesic foliation of codimension one. We give, up to universal covering, a complete local classification of such hypersurfaces within the de Sitter space, identifying new examples distinct from those found in the Riemannian and flat Lorentzian space forms. Additionally, we present diverse examples of such hypersurfaces along with some partial classification in the anti-de Sitter space, illustrating their varied nature.</p>

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Hypersurfaces in Non-Flat Lorentzian Space Forms with a Totally Geodesic Foliation of Codimension One

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • N. Heidari,
  • S. M. B. Kashani,
  • M. J. Vanaei

摘要

In this paper we investigate hypersurfaces in non-flat Lorentzian space forms that carry a totally geodesic foliation of codimension one. We give, up to universal covering, a complete local classification of such hypersurfaces within the de Sitter space, identifying new examples distinct from those found in the Riemannian and flat Lorentzian space forms. Additionally, we present diverse examples of such hypersurfaces along with some partial classification in the anti-de Sitter space, illustrating their varied nature.