First eigenvalue of Schrödinger operator of space-like hypersurfaces. (English) Zbl 1333.53097
Summary: We introduce two Schrödinger operators of compact space-like hypersurfaces in a de Sitter space. If the hypersurfaces have constant mean curvature or constant scalar curvature, we obtain some spectral characterisations of totally umbilical space-like hypersurfaces by the first eigenvalue of the Schrödinger operators.
MSC:
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 35J10 | Schrödinger operator, Schrödinger equation |
