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Graphic Bernstein results in curved pseudo-Riemannian manifolds. (English) Zbl 1173.53031
The classical Bernstein theorem has been generalized to graphic hypersurfaces of \(\mathbb R^{m+1}\) for \(m\leq 7\), and for higher dimensions and codimensions under various growth conditions. In the paper [J. Geom. Phys. 59, No. 5, 620–631 (2009; Zbl 1173.53025)], A. Albujer and L. Alias have proved a new Calabi-Bernstein-type result for surfaces immersed into a Lorentzian product 3-manifold of the form \(\Sigma_1\times\mathbb R\), where \(\Sigma_1\) is a Riemannian surface of nonnegative Gauss curvature. In this paper the authors generalize this result to space-like graphic submanifolds with parallel mean curvature in a non-flat pseudo-Riemannian product space of any dimension \(m+n\) and under less restrictive curvature condition.

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