Bernstein-type theorems in semi-Riemannian warped products
F. Camargo,Antonio Caminha,H.F. de Lima +2 more
- Vol. 139, Iss: 5, pp 1841-1850
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In this article, complete hypersurfaces immersed in the (n + 1)-dimensional hyperbolic and steady state spaces were studied and Bernstein-type results were obtained for these ambient spaces.Abstract:
This paper deals with complete hypersurfaces immersed in the (n + 1)-dimensional hyperbolic and steady state spaces. By applying a technique of S. T. Yau and imposing suitable conditions on both the r-th mean curvatures and on the norm of the gradient of the height function, we obtain Bernstein-type results in each of these ambient spaces.read more
Citations
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On the rigidity of constant mean curvature complete vertical graphs in warped products
Cícero P. Aquino,H.F. de Lima +1 more
TL;DR: In this article, the authors investigate constant mean curvature complete vertical graphs in a warped product, which is supposed to satisfy an appropriated convergence condition, and obtain rigidity theorems concerning to such graphs.
Journal ArticleDOI
Generalized maximum principles and the rigidity of complete spacelike hypersurfaces
TL;DR: In this paper, the uniqueness of complete, non-compact spacelike hypersurfaces immersed in a class of Lorentzian warped products obeying a suitable convergence condition is studied.
Journal ArticleDOI
Some rigidity theorems in semi-Riemannian warped products
Journal ArticleDOI
On the Unicity of Complete Hypersurfaces Immersed in a Semi-Riemannian Warped Product
Cícero P. Aquino,H.F. de Lima +1 more
TL;DR: In this paper, the unicity of complete hypersurfaces immersed in a semi-Riemannian warped product is studied and sufficient conditions to guarantee that such a hypersurface must be a slice are established.
Journal ArticleDOI
On the rigidity of complete spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime
TL;DR: In this article, the uniqueness of complete noncompact spacelike hypersurfaces immersed in a generalized Robertson-Walker spacetime was studied and a suitable restriction on the norm of the gradient of the height function of the hypersurface was proposed.
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Semi-Riemannian Geometry
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