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<p>Our purpose is to investigate geometric aspects of complete and stochastically complete CMC spacelike hypersurfaces immersed into a class of Lorentzian Einstein manifolds satisfying appropriate curvature constraints. Assuming that the total umbilicity tensor satisfies an Okumura type inequality, we derive a suitable Simons type inequality which, jointly with several maximum principles and certain integrability conditions, enable us to establish rigidity and nonexistence results concerning these spacelike hypersurfaces.</p>

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Rigidity and nonexistence of CMC spacelike hypersurfaces via an Okumura type inequality in a class of Lorentzian Einstein manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月7日

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  • Henrique F. de Lima,
  • Ary V. F. Leite,
  • Marco A. L. Velásquez

摘要

Our purpose is to investigate geometric aspects of complete and stochastically complete CMC spacelike hypersurfaces immersed into a class of Lorentzian Einstein manifolds satisfying appropriate curvature constraints. Assuming that the total umbilicity tensor satisfies an Okumura type inequality, we derive a suitable Simons type inequality which, jointly with several maximum principles and certain integrability conditions, enable us to establish rigidity and nonexistence results concerning these spacelike hypersurfaces.