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Investigation of geometric properties reveals rigidity and nonexistence of CMC hypersurfaces, indicating important constraints.
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.
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Lima et al. (2026) studied this question.
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