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ON THE UMBILICITY OF HYPERSURFACES IN THE HYPERBOLIC SPACE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 103 / Issue 1 / August 2017
- Published online by Cambridge University Press:
- 16 November 2016, pp. 45-58
- Print publication:
- August 2017
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- Article
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In this paper, we establish new characterization results concerning totally umbilical hypersurfaces of the hyperbolic space
$\mathbb{H}^{n+1}$, under suitable constraints on the behavior of the Lorentzian Gauss map of complete hypersurfaces having some constant higher order mean curvature. Furthermore, working with different warped product models for 
$\mathbb{H}^{n+1}$ and supposing that certain natural inequalities involving two consecutive higher order mean curvature functions are satisfied, we study the rigidity and the nonexistence of complete hypersurfaces immersed in 
$\mathbb{H}^{n+1}$.
