Constant curvature spacelike hypersurfaces in the Lorentz-Minkowski space. (English) Zbl 0979.53069

Alías, Luis J.; Pastor, José A.

Mladenov, I. M. (ed.) et al., Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, September 1-10, 1999. Sofia: Coral Press Scientific Publishing. 17-26 (2000).

The authors demonstrate some results about compact spacelike hypersurfaces with spherical boundary in \(L^{n+1}\). The authors prove:
Theorem 1. The only compact spacelike hypersurfaces in the Lorentz-Minkowski space with constant mean curvature and spherical boundary are the hyperplanar balls and the hyperbolic caps.
Theorem 2. The only compact spacelike hypersurfaces in the Lorentz-Minkowski space with nonzero constant scalar curvature and spherical boundary are the hyperbolic caps.
For the entire collection see [Zbl 0940.00039].

Reviewer: V.T.Fomenko (Taganrog)

MSC:

53C42	Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Keywords:

compact spacelike hypersurfaces; constant mean curvature; hyperplanar balls; hyperbolic caps; constant scalar curvature