Complete space-like hypersurfaces in locally symmetric Lorentz spaces. (English) Zbl 1078.53055
Two theorems about complete space-like hypersurfaces with constant mean curvature in a locally symmetric Lorentz space are the main results of this paper. Under some conditions for the sectional curvature, several estimates of the squared norm of the second fundamental form for such hypersurfaces are obtained and totally umbilical hypersurfaces are characterized.
Reviewer: Radu Miron (Iaşi)
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
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