Rigidity and nonexistence of CMC spacelike hypersurfaces via an Okumura type inequality in a class of Lorentzian Einstein manifolds
Abstract
Abstract 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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Geometry and complex manifolds
Publication details
- Journal / source
- manuscripta mathematica
- Volume
- 177
- Issue
- 1
- Publication date
- 1 February 2026
- Language
- EN